Exhibit 4.2

EXECUTION VERSION

OFFSHORE GROUP INVESTMENT LIMITED

AND EACH OF THE GUARANTORS PARTY HERETO

11  ¹/2% SENIOR SECURED FIRST LIEN NOTES DUE 2015

FOURTH SUPPLEMENTAL INDENTURE

Dated as of April 2, 2012

Wells Fargo Bank, National Association,

as Trustee and Noteholder Collateral Agent

THIS FOURTH SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as of April 2, 2012, is by and among Offshore Group Investment Limited, a Cayman Islands exempted company (the “Company”), Vantage Drilling Company, a Cayman Islands exempted company (“Parent”), as a guarantor, Dragonquest Holdings Company, a Cayman Islands exempted company (“Dragonquest Holdings”), Valencia Drilling Poland sp. z o.o. (to be renamed Vantage Drilling Poland sp. z o.o.) (“Vantage Drilling Poland”), Dragonquest Holdings Cyprus ODC Limited (to be renamed Vantage Holdings Cyprus ODC Limited), a company incorporated in the Republic of Cyprus (“Vantage Holdings Cyprus”, and together with Dragonquest Holdings and Vantage Drilling Poland, the “Additional Guarantors”), the other existing guarantors to the Indenture (as defined below) (the “Existing Guarantors”, together with Parent and the Additional Guarantors, the “Guarantors”) and Wells Fargo Bank, National Association, and any and all successors thereto, as trustee (in such capacity, the “Trustee”) and as collateral agent (in such capacity, the “Noteholder Collateral Agent”).

WHEREAS, the Company, the Guarantors and the Trustee and Noteholder Collateral Agent have executed and delivered that certain Indenture dated as of July 30, 2010 (the “Original Indenture”), providing for the issuance of the Company’s 11 ¹/2% Senior Secured First Lien Notes due 2015 (the “Notes”), as amended by the First Supplemental Indenture dated as of May 20, 2011 (the “First Supplemental Indenture”), the Second Supplemental Indenture dated as of June 1, 2011 (the “Second Supplemental Indenture”) and the Third Supplemental Indenture dated as of June 29, 2011 (the “Third Supplemental Indenture” together with the Original Indenture, First Supplemental Indenture and Second Supplemental Indenture, the “Indenture”);

WHEREAS, Section 9.01 of the Indenture provides that the Indenture or the Notes may be amended without the consent of any Holder to, among other things, cure any ambiguity, defect or inconsistency;

WHEREAS, Section 9.02 of the Indenture provides that the Indenture or the Notes may be amended with the consent of Holders representing at least a majority in principal amount of the Notes then outstanding (including, without limitation, consents obtained in connection with a purchase of, or tender offer or exchange offer for, Notes);

WHEREAS, the Company has solicited consents, in accordance with Section 9.02 of the Indenture, from the Holders for certain proposed amendments (the “Proposed Amendments”) to the Indenture and the Notes pursuant to the Consent Solicitation Statement dated March 22, 2012 (as the same may be amended or supplemented from time to time, the “Statement”), which Proposed Amendments are contained in this Supplemental Indenture;

WHEREAS, (i) the Company has received the written consent of the Holders of more than a majority in principal amount of the outstanding Notes to the Proposed Amendments, all as certified by an Officers’ Certificate delivered to the Trustee simultaneously with the execution and delivery of this Supplemental Indenture, (ii) the Company has delivered to the Trustee and Noteholder Collateral Agent simultaneously with the execution and delivery of this Supplemental Indenture an Opinion of Counsel relating to this Supplemental Indenture as contemplated by Sections 9.06, 13.04 and 13.05 of the Indenture and (iii) the Company and the Guarantors have satisfied, performed and complied with all other conditions required under Article 9 of the Indenture to enable the Company, the Guarantors and the Trustee and Noteholder Collateral Agent to enter into this Supplemental Indenture and to make this Supplemental Indenture a valid and binding agreement of the Company and the Guarantors;

2

WHEREAS, the Indenture provides that under certain circumstances certain Subsidiaries of Parent or the Company will be required to become a guarantor under the Indenture and that such additional guarantors will, among other things execute and deliver to the Trustee a supplemental indenture and Note Guarantee pursuant to which each such additional guarantor shall unconditionally guarantee all of the Company’s Obligations under the Notes and the Indenture on the terms and conditions set forth herein and therein;

WHEREAS, pursuant to Sections 9.01, 9.02 and 9.06 of the Indenture, the Trustee and Noteholder Collateral Agent is authorized to execute and deliver this Supplemental Indenture; and

WHEREAS, the Company desires to enter into, and, pursuant to the foregoing authority, has requested the Trustee and Noteholder Collateral Agent to join with it and the Guarantors in entering into, this Supplemental Indenture for the purpose of amending the Indenture and the Notes in certain respects as permitted by Sections 9.01 and 9.02 of the Indenture.

NOW, THEREFORE, in consideration of the above premises, each party hereby agrees, for the benefit of the others and for the equal and ratable benefit of the Holders, as follows:

ARTICLE I

AMENDMENTS TO THE INDENTURE AND THE NOTES

Section 1.1 Amendments to the Indenture and Notes. The Indenture and the Notes are hereby amended by:

(a) amending Section 1.01 to add the definition of “Bridge Loan Lender” as follows:

“ “Bridge Loan Lender” means Standard Chartered Bank, Offshore Banking Unit (or Standard Chartered Bank (Hong Kong) Limited as administrative agent on its behalf).”

(b) amending Section 1.01 to add the definition of “Dragonquest” as follows:

“ “Dragonquest” means the Ultra Deepwater Drillship Hull No. 3602 currently under construction at DSME, with delivery expected in April 2012, to be owned by the Company or a Restricted Subsidiary, and to be registered in the name of the Company or a Restricted Subsidiary under Bahamian flag.”

(c) amending Section 1.01 to add the definition of “Dragonquest Accounts Assignment” as follows:

“ “Dragonquest Accounts Assignment” means, collectively, the first priority assignments of the Dragonquest Escrow Account in favor of the Noteholder Collateral Agent given by the Company, each Guarantor and each Internal Charterer, as the same may be amended, supplemented or modified from time to time.”

3

(d) amending Section 1.01 to add the definition of “Dragonquest Acquisition” as follows:

“ “Dragonquest Acquisition” means (a) the purchase from Valencia of all of the rights and obligations under the Dragonquest Construction Contract pursuant to a Purchase Agreement dated March 20, 2012 and the purchase of related equipment specified in such Purchase Agreement, and including, pursuant to the terms of the Purchase Agreement, the repayment to the Bridge Loan Lender of amounts owed to such Bridge Loan Lender by Valencia in connection with Valencia’s financing of a portion of the construction costs and expenses of the Dragonquest and (b) the entry into and performance of the ancillary documents entered into in connection with the Purchase Agreement.”

(e) amending Section 1.01 to add the definition of “Dragonquest Construction Assignment” as follows:

“ “Dragonquest Construction Assignment” means the first priority Assignment of the Dragonquest Construction Contract and Dragonquest Refund Guarantee in favor of the Noteholder Collateral Agent given by Dragonquest Holdings Company respecting the Dragonquest Construction Contract (including the Dragonquest Refund Guarantee) together with the consent thereto, if any, of each of DSME and Korea Exim Bank, as issuer of the Dragonquest Refund Guarantee, as amended, modified or supplemented from time to time; provided, however, that the Assignment of the Dragonquest Refund Guarantee shall not be required to be delivered as Collateral if delivery and acceptance of the Dragonquest in conformity with the requirements of the Dragonquest Construction Contract occurs concurrently with the release of the Dragonquest Escrowed Proceeds from the Dragonquest Escrow Account.”

(f) amending Section 1.01 to add the definition of “Dragonquest Construction Contract” as follows:

“ “Dragonquest Construction Contract” means the Construction Contract between DSME and Valencia Drilling Corporation dated December 27, 2007, respecting the construction and delivery of the Dragonquest, as amended, modified, or supplemented from time to time.”

(g) amending Section 1.01 to add the definition of “Dragonquest Construction Payments” as follows:

“ “Dragonquest Construction Payments” means one or more payments in respect of the Dragonquest paid or payable on or prior to the time of delivery and acceptance of the Dragonquest in conformity with the requirements of the Dragonquest Construction Contract and the specifications set forth therein.”

4

(h) amending Section 1.01 to add the definition of “Dragonquest Delivery Date” as follows:

“ “Dragonquest Delivery Date” has the meaning set forth in Section 4.23(a).”.

(i) amending Section 1.01 to add the definition of “Dragonquest Escrow Account” as follows:

“ “Dragonquest Escrow Account” means the escrow account established and governed by the Dragonquest Escrow Agreement.”

(j) amending Section 1.01 to add the definition of “Dragonquest Escrow Agreement” as follows:

“ “Dragonquest Escrow Agreement” has the meaning set forth in Section 3.11(a).”

(k) amending Section 1.01 to add the definition of “Dragonquest Escrowed Proceeds” as follows:

“ “Dragonquest Escrowed Proceeds” has the meaning set forth in Section 3.11(a).”

(l) amending Section 1.01 to add the definition of “Dragonquest Refund Guarantee” as follows:

“ “Dragonquest Refund Guarantee” means the Letter of Credit issued by the Korea Eximbank, or similar instrument respecting the obligations of DSME under the Dragonquest Construction Contract, as amended, modified or supplemented from time to time.”

(m) amending Section 1.01 to add the definition of “Dragonquest Transaction Fees” as follows:

“ “Dragonquest Transaction Fees” means (a) the consent fee paid to holders of outstanding Notes in connection with the Solicitation and (b) the fees and expenses in connection with (i) the issuance and sale of the Additional Notes referred to in Section 4.08(b)(16), (ii) the Solicitation, (iii) the Dragonquest Acquisition, (iv) the funding of the Dragonquest Construction Payments and (v) all other transactions relating to the foregoing.”

(n) amending Section 1.01 to add the definition of “Dragonquest Transactions” as follows:

“ “Dragonquest Transactions” means, collectively, (a) funding of the Dragonquest Escrow Account, (b) the Dragonquest Acquisition, (c) funding of the Dragonquest Construction Payments, (d) satisfaction of the Reimbursement Obligations, (e) payment of the Dragonquest Transaction Fees and (f) all other transactions relating to the foregoing.”

5

(o) amending Section 1.01 to add the definition of “Petrobras” as follows:

“ “Petrobras” means Petrobras Venezuela Investments & Services B.V., a company organized and established under the laws of the Netherlands, and its successors and assigns.”

(p) amending Section 1.01 to add the definition of “Petrobras Drilling Contract” as follows:

“ “Petrobras Drilling Contract” means the Drilling Contract, dated as of February 4, 2009, by and between Petrobras and Vantage Deepwater Company, as the same may be amended, supplemented or modified from time to time.”

(q) amending Section 1.01 to add the definition of “Petrobras Extension” as follows:

“ “Petrobras Extension” has the meaning set forth in Section 3.11(b)(3).”

(r) amending and restating the definition of “Registration Rights Agreement” of Section 1.01 as follows:

“ “Registration Rights Agreement” means the Registration Rights Agreement entered into as of the Issue Date among the Representatives, the Company and the Guarantors and any other Registration Rights Agreement entered into from time to time in connection with the issuance of Additional Notes under the Indenture.”

(s) amending Section 1.01 to add the definition of “Reimbursement Obligations” as follows:

“ “Reimbursement Obligations” has the meaning set forth in Section 3.11(a).”

(t) deleting the definition of “Representative” of Section 1.01.

(u) amending Section 1.01 to add the definition of “Representatives” as follows:

“ “Representative” means (a) with respect to the issuance of the Initial Notes on the Issue Date, Jefferies & Company, Inc. and Deutsche Bank Securities Inc., and (b) with respect to any issuance of Additional Notes, any one or more initial purchasers acting in such role pursuant to a purchase agreement entered into with the Company and the Guarantors.”

6

(v) amending and restating the definition of “Ship Mortgage” of Section 1.01 as follows:

“ “Ship Mortgage” means collectively the first naval mortgages and other instruments such as statutory mortgages and deeds over the Vessels (including, with respect to the Dragonquest, executed, delivered, and recorded as of the date the Dragonquest is delivered by DSME to the applicable Guarantor), each duly registered in the Bahamian or Panamanian ship registry, as applicable, in favor of the Noteholder Collateral Agent, as the same may be amended, supplemented or modified from time to time.”.

(w) amending Section 1.01 to add the definition of “Solicitation” as follows:

“ “Solicitation” means the solicitation of consents by the Company, Parent and the other Guarantors, upon the terms and subject to the conditions set forth in the Consent Solicitation Statement dated March 22, 2012 and in the accompanying Letter of Consent, as the same may be amended or supplemented from time to time.”

(x) amending and restating the definition of “Special Mandatory Redemption” as follows:

“ “Special Mandatory Redemption” is the redemption provision set forth under Sections 3.09 (“Special Mandatory Redemption”) and 3.11 (“Escrow and Special Mandatory Redemption Related to the Dragonquest”)”.

(y) amending Section 1.01 to add the definition of “Valencia” as follows:

“ “Valencia” means Valencia Drilling Corporation, a corporation organized under the laws of the Marshall Islands and an affiliate of F3 Capital.”

(z) amending and restating the definition of “Vessels” as follows:

“ “Vessels” means (i) the Panamanian flag vessels the Emerald Driller, the Sapphire Driller, the Topaz Driller and the Aquamarine Driller, (ii) the Bahamian flag vessels the Platinum Explorer and, upon the delivery to the applicable Guarantor, the Dragonquest, and (iii) any other vessel hereafter acquired by the Company or any Restricted Subsidiary”.

(aa) amending Article III to add the section of “Section 3.11 Escrow and Special Mandatory Redemption Related to the Dragonquest” as follows:

“Section 3.11 Escrow and Special Mandatory Redemption Related to the Dragonquest

(a) Upon the closing of the offering of the Additional Notes issued pursuant to Section 4.08(b)(16), the Company shall cause the proceeds, net of Dragonquest Transaction Fees (the “Dragonquest Escrowed Proceeds”), to be deposited directly into the Dragonquest Escrow Account to be established by the Noteholder Collateral Agent pursuant to an escrow agreement (the “Dragonquest Escrow Agreement”). The Dragonquest Escrowed Proceeds (or portions thereof)

7

may be released to, or as directed by, the Company, for the following purposes, which must occur substantially concurrently: (i) to fund the Dragonquest Acquisition, (ii) to fund the Dragonquest Construction Payments, (iii) to reimburse and pay for construction costs, expenses and other expenditures previously incurred, and to be incurred on or prior to the commencement of operations of the Dragonquest, in each case, on an arm’s length basis, in good faith and in the ordinary course of business by Parent or a Subsidiary of Parent for the purpose of making the Dragonquest operational (the “Reimbursement Obligations”) and (iv) for general corporate purposes.

(b) The conditions to the release of the Dragonquest Escrowed Proceeds shall include the conditions set forth in the Dragonquest Escrow Agreement, including the following:

(1) the Company complying with the terms of the Dragonquest Construction Contract, such that, upon payment of the Dragonquest Construction Payments, DSME shall be prepared to deliver the Dragonquest to the Company, or a Subsidiary designated by the Company, in conformity with the specifications set forth in the Dragonquest Construction Contract;

(2) amounts due to the Bridge Loan Lender in connection with their loan to Valencia to fund certain construction costs for the Dragonquest shall have been repaid in full and all related liens held by the Bridge Loan Lender shall have been released (in each case contemporaneous with the release and use of such portion of the Dragonquest Escrowed Proceeds); and

(3) entry into a written, legally binding amendment to the Petrobras Drilling Contract that provides for an extension of the commencement date deadline of the Petrobras Drilling Contract to a date at least (x) 120 days from the actual delivery and acceptance date of the Dragonquest, which is expected to be in April 2012, and (y) September 25, 2012, whichever is the later (the “Petrobras Extension”).”

(c) The Company shall be required to redeem in full the Additional Notes incurred pursuant to Section 4.08(b)(16) at a redemption price equal to the offering price plus 1% thereon and accrued and unpaid interest to the redemption date, upon the first to occur of any of the following events:

(1) prior to the delivery and acceptance of the Dragonquest in conformity with the Dragonquest Construction Contract and the specifications set forth therein, the Dragonquest Construction Contract is terminated for any reason, or amended or modified after the issue date of the Additional Notes incurred pursuant to Section 4.08(b)(16) in any manner materially adverse to the Company or any of the Restricted Subsidiaries or the holders of the Notes; or

8

(2) prior to the delivery and acceptance of the Dragonquest in conformity with the Dragonquest Construction Contract and the specifications set forth therein, the Petrobras Drilling Contract is terminated for any reason or amended or modified after the issue date of the Additional Notes incurred pursuant to Section 4.08(b)(16) in any manner materially adverse to the Company or any of the Restricted Subsidiaries or the holders of the Notes; or

(3)       (A) delivery to and acceptance of the Dragonquest by the Company or the applicable Restricted Subsidiary in conformity with the requirements of the Dragonquest Construction Contract and the specifications set forth therein has not occurred;

(B) good and marketable title for the Dragonquest and the Dragonquest Construction Contract, including the release of all related liens held by the Bridge Loan Lender, is not transferred to the Company or the applicable Restricted Subsidiary;

(C) the Dragonquest is not registered in the name of the Company or the applicable Restricted Subsidiary as owner under Bahamian flag; or

(D) a Ship Mortgage is not recorded on the Dragonquest in favor of the Noteholder Collateral Agent,

in each case with respect to each of the items in this clause (3) by the later of (i) June 30, 2012 and (ii) if the Company and Petrobras have agreed in writing to a modified Petrobras Extension that permits a later commencement date deadline under the Petrobras Drilling Contract, June 30, 2012 plus the number of days so extended up to a maximum of 30 days.

(d) Other than as specifically provided in this Section 3.11, any redemption pursuant to this Section shall be made pursuant to the provisions of Sections 3.01 (“Notices to Trustee”) through 3.06 (“Notes Redeemed or Purchased in Part”), as applicable.”

(bb) amending Section 4.08(b) as follows:

(i) delete “and” from the end of subsection (14);

(ii) replace “.” with “; and” at the end of subsection (15); and

(iii) add a new subsection (16) as follows:

“(16) the incurrence by the Company and the Guarantors of additional Indebtedness represented by the Additional Notes not to exceed $775.0 million in aggregate principal amount and the related Note Guarantees for the purpose of consummating the Dragonquest Transactions.”.

9

(cc) amending Section 4.11(b) as follows:

(i) delete the word “and” at the end of subsection (10);

(ii) add the word “and” at the end of subsection (11); and

(iii) add the following subsection (12) as follows:

“(12) (a) the Dragonquest Acquisition with Valencia and any other applicable Affiliate of Valencia, provided that Parent receives an opinion that the purchase price to be paid to Valencia in the Dragonquest Acquisition is fair to the disinterested stockholders of Parent from a financial point of view issued by an accounting, appraisal or investment banking firm of national standing, and based on such opinion, the Board of Directors of Parent approves the Dragonquest Acquisition; and (b) the Reimbursement Obligations.”.

(dd) amending Section 4.21(g) to delete “The Company or Parent” from the beginning of the sub-section and replace with “The Company or the Guarantors”.

(ee) adding Section 4.23 as follows:

“Section 4.23 Dragonquest Delivery Date

(a) On the date (the “Dragonquest Delivery Date”) on which the Dragonquest is delivered (unless otherwise provided below) by DSME to, and accepted by the Company or a Subsidiary of the Company, or any branch or office thereof, the Company covenants and agrees to execute and deliver, or to cause to be executed and delivered, and to do, or cause to be done, the documents or actions set out below:

(1) Delivery to the Noteholder Collateral Agent, in form reasonably satisfactory to the Noteholder Collateral Agent, of:

(A) a copy of the Protocol of Delivery and Acceptance respecting the Dragonquest executed by (i) DSME and (ii) the Company or a Subsidiary of the Company, or any branch or office thereof;

(B) a copy of the full warranty Bill of Sale and Builder’s Certificate respecting the Dragonquest and if delivery is made by DSME to any entity other than Vantage Drilling Poland – Luxembourg Branch, a bill of sale from such entity to Vantage Drilling Poland – Luxembourg Branch and a warranty of good title and freedom from liens from any such entity that has intermediate title;

(C) a copy of the interim class certificate;

(D) a copy of the Bahamian Certificate of Registry respecting the Dragonquest;

10

(E) a copy of the Bahamian Transcript of Registry issued by the appropriate Bahamian authorities evidencing registration of the Dragonquest under Bahamian flag in the name of Vantage Drilling Poland – Luxembourg Branch and the recordation of the Ship Mortgage;

(F) a copy of the Dragonquest Construction Assignment as novated from Valencia to Dragonquest Holdings Company and/or a copy of the Deed of Assignment from Valencia to Dragonquest Holdings Company;

(G) a copy of the Ship Mortgage (including deed of covenants) covering the Dragonquest duly executed by Vantage Drilling Poland – Luxembourg Branch (and in respect of the deed of covenants only also the Noteholder Collateral Agent ) and duly filed with the Bahamian authorities;

(H) (a) evidence of insurance respecting the Dragonquest that complies with the insurance requirements set forth in the Collateral Agreements, including copies of cover notes (with loss payable clause and notice of assignment attached), letter from protection and indemnity club, and letter detailing the insurances from the Company’s independent marine insurance broker and (b) a favorable report from the Insurance Advisor addressed to the Noteholder Collateral Agent stating that the insurances covering the Dragonquest (x) comply with the requirements of the Ship Mortgage and (y) are sufficient in form and substance to protect the interests of the Trustee, Noteholder Collateral Agent and the Holders.

(I) a copy of a duly executed Internal Charter to cover any and all the bareboat charters respecting the Dragonquest;

(J) a copy of the duly executed Drilling Contract, as amended, between Vantage Deepwater Company and Petrobras respecting the Dragonquest;

(K) a certificate of the Company stating that the Dragonquest is subject to an Internal Charter between Vantage Deepwater Company, as Internal Charterer, and Vantage Drilling Poland – Luxembourg Branch, as the Vessel owner, together with (A) a copy of the Internal Charter respecting the Dragonquest; (B) an appropriate Earnings Assignment and Insurance Assignment (and the Internal Charterer shall also have executed and delivered an Insurance Assignment and an Earnings Assignment); and (C) a copy of the Petrobras Drilling Contract between Vantage Deepwater Company and Petrobras certified as true, correct and complete and no default or event of default has occurred and is existing thereunder;

(L) an opinion of the Company’s Bahamian legal counsel, in the form attached hereto as Exhibit M;

11

(M) a bring-down opinion of the Company’s Cayman Islands legal counsel, in the form attached hereto as Exhibit N; and

(N) any additional Uniform Commercial Code, Companies’ Registry or other similar filings or notices or recordings requested by the Trustee or Noteholder Collateral Agent to perfect the security interests or Liens granted, or intended to be granted, by any Collateral Agreement.

(b) As of the date the Petrobras Drilling Contract is novated to Vantage Deepwater Drilling, Inc., a certificate of the Company stating that the Dragonquest is subject to an Internal Charter between Vantage Deepwater Drilling, Inc, as Internal Charterer, and Vantage Drilling Poland – Luxembourg Branch, as the Vessel owner, together with (A) a copy of the Internal Charter respecting the Dragonquest; (B) an appropriate Earnings Assignment and Insurance Assignment (and the Internal Charterer shall also have executed and delivered an Insurance Assignment and an Earnings Assignment); (C) a copy of the Petrobras Drilling Contract between Vantage Deepwater Drilling, Inc. and Petrobras certified as true, correct and complete and no default or event of default has occurred and is existing thereunder; and (D) an opinion of the Company’s Delaware counsel, in the form attached hereto as Exhibit O.”

(ff) amending and restating Section 6.01(3) as follows:

“(3) failure by Parent, the Company, any of the Restricted Subsidiaries or any Other Guarantor, as the case may be, to timely offer to purchase, purchase and pay for Notes as required by the provisions of Section 3.09 (“Special Mandatory Redemption”), Section 3.11 (“Escrow and Special Mandatory Redemption Related to the Dragonquest”), Section 4.17 (“Offer to Repurchase Upon Change of Control”), Section 4.18 (“Asset Sales”) or Section 4.19 (“Excess Cash Flow Offer”) or to comply with the provisions of Section 4.07 (“Restricted Payments”), Section 4.08 (“Incurrence of Indebtedness and Issuance of Preferred Stock”) or Section 5.01 (“Merger, Consolidation, or Sale of Assets”);

(gg) amending Section 9.01 as follows:

(i) delete the word “or” at the end of subsection (13);

(ii) delete “.” and add the “;” at the end of subsection (14);

(iii) add the following subsection (15) as follows:

“(15) to enter into, and to perfect security interests and Liens granted therein, the Collateral Agreements and transactions contemplated thereby respecting Bahamian registration of the Dragonquest and its mortgaging after the Issue Date; or”; and

(iv) add the following subsection (16) as follows:

12

“(16) to accept and consent to, and to take all steps to perfect a security interest under, Collateral Agreements to be granted subsequent to the Issue Date respecting the Dragonquest Construction Contract, Drilling Contracts and Internal Charters covering the Dragonquest.”.

(hh) amending Section 9.02 (2) to insert, following the phrase “Section 3.09 (Special Mandatory Redemption)”, the phrase and punctuation, “Section 3.11 (Escrow and Special Mandatory Redemption Related to the Dragonquest),”.

(ii) amending Section 9.02 (7) to insert, following the phrase “Section 3.09 (Special Mandatory Redemption)”, the phrase and punctuation, “Section 3.11 (Escrow and Special Mandatory Redemption Related to the Dragonquest),”.

(jj) amending Section 12.01(a)(2)(B) to:

(i) replace “and” after “Section 4.20 (“Impairment of Security Interest”)” with “,”; and

(ii) add “and Section 4.23 (“Dragonquest Delivery Date”)”“ after “Section 4.22 (“Platinum Explorer Delivery Date”)”.

(kk) amending Section 12.03(a) to:

(i) delete “or” from the end of subsection (6);

(ii) replace “.” with “; or” at the end of subsection (7); and

(iii) add a new subsection (8) as follows:

“(8) with respect to the Dragonquest Escrowed Proceeds, upon release of all Dragonquest Escrowed Proceeds for the purposes specified under Section 3.11”.

(i) replace “or” from the end of (i) with “,”; and

(ii) replace “.” with “or (iii) any amendment to, or other agreement in respect of, the Dragonquest Construction Contract to the extent that any such amendment or agreement would be materially adverse to the Company or any of the Restricted Subsidiaries or the holders of the notes.” at the end of (ii).

13

Section 1.2 Additional Amendments. Any and all additional provisions of the Indenture and the Notes are hereby deemed to be amended to reflect the intentions of the amendments provided for in this Article I.

ARTICLE II

ADDITIONAL GUARANTORS

Section 2.1 Agreement to Guarantee. Each of the Additional Guarantors hereby agrees to provide an unconditional Note Guarantee on the terms and subject to the conditions set forth in the Note Guarantee and the Indenture, including but not limited to Section 4.13 and Article 11 thereof, and subject to the limitations therein.

ARTICLE III

MISCELLANEOUS PROVISIONS

Section 3.1 Defined Terms. For all purposes of this Supplemental Indenture, except as otherwise defined or unless the context otherwise requires, terms used in capitalized form in this Supplemental Indenture and defined in the Indenture have the meanings specified in the Indenture.

Section 3.2 Indenture. Except as expressly amended hereby, the Indenture and the Notes are in all respects ratified and confirmed and all the terms shall remain in full force and effect. This Supplemental Indenture shall form a part of the Indenture for all purposes, and every Holder heretofore or hereafter authenticated and delivered under the Indenture shall be bound hereby and all terms and conditions of both shall be read together as though they constitute a single instrument.

Section 3.3 Governing Law. THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

Section 3.4 Successors. All agreements of the Company and the Guarantors in this Supplemental Indenture and the Notes shall bind their respective successors. All agreements of the Trustee and Noteholder Collateral Agent in this Supplemental Indenture shall bind their successors.

Section 3.5 Duplicate Originals. All parties may sign any number of copies of this Supplemental Indenture. Each signed copy shall be an original, but all of them together shall represent the same agreement. It is the express intent of the parties to be bound by the exchange of signatures on this Supplemental Indenture via telecopy or other form of electronic transmission.

Section 3.6 Severability. In case any one or more of the provisions in this Supplemental Indenture shall be held invalid, illegal or unenforceable, in any respect for any reason, the validity, legality and enforceability of any such provision in every other respect and of the remaining provisions shall not in any way be affected or impaired thereby, it being intended that all of the provisions hereof shall be enforceable to the full extent permitted by law.

14

Section 3.7 Trustee Disclaimer. The Trustee and Noteholder Collateral Agent accepts the amendments of the Indenture effected by this Supplemental Indenture and agrees to execute the trust created by the Indenture as hereby amended, but on the terms and conditions set forth in the Indenture, including the terms and provisions defining and limiting the liabilities and responsibilities of the Trustee and Noteholder Collateral Agent, which terms and provisions shall in like manner define and limit its liabilities and responsibilities in the performance of the trust created by the Indenture as hereby amended, and without limiting the generality of the foregoing, the Trustee and Noteholder Collateral Agent shall not be responsible in any manner whatsoever for or with respect to any of the recitals or statements contained herein, all of which recitals or statements are made solely by the Company and the Guarantors, and the Trustee and Noteholder Collateral Agent make no representation with respect to any such matters. Additionally, the Trustee and Noteholder Collateral Agent make no representations as to the validity or sufficiency of this Supplemental Indenture.

Section 3.8 Effectiveness. The Proposed Amendments effected by this Supplemental Indenture shall take effect immediately upon the provision by the Company to the Trustee of an Officers’ Certificate certifying that the conditions set forth in the Company’s Consent Solicitation Statement dated March 22, 2012, as amended or supplemented from time to time, have been either satisfied or, where permitted, waived by the Company and the delivery to the Trustee of the Officers’ Certificates and Opinions of Counsel described in Section 9.06 of the Indenture.

Section 3.9 Supplemental Indenture Controls. In the event there is any conflict or inconsistency between the Indenture and this Supplemental Indenture, the provisions of this Supplemental Indenture shall control.

Section 3.10 Effect of Headings. The Section headings herein are for convenience only and shall not affect the construction thereof.

[THE REMAINDER OF THIS PAGE IS INTENTIONALLY LEFT BLANK]

15

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed as of the day and year written above.

[Signature Page to Fourth Supplemental Indenture]

[Signature Page to Fourth Supplemental Indenture]

[Signature Page to Fourth Supplemental Indenture]

[Signature Page to Fourth Supplemental Indenture]

[Signature Page to Fourth Supplemental Indenture]

[Signature Page to Fourth Supplemental Indenture]