Exhibit 4.2

Execution Version

CONTINENTAL AIRLINES, INC.,

AS ISSUER,

TO

WILMINGTON TRUST COMPANY,

AS TRUSTEE

FIRST SUPPLEMENTAL INDENTURE

DATED OCTOBER 1, 2010

SUPPLEMENTING AND AMENDING THE INDENTURE

DATED AS OF NOVEMBER 10, 2000

(6% Convertible Junior Subordinated Debentures due 2030)

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THIS FIRST SUPPLEMENTAL INDENTURE, dated as of October 1, 2010, (hereinafter called the “Supplemental Indenture”), is between CONTINENTAL AIRLINES, INC., a Delaware corporation (hereinafter called the “Company”), UNITED CONTINENTAL HOLDINGS, INC., a Delaware corporation (hereinafter called “UAL”) formerly known as UAL Corporation, and WILMINGTON TRUST COMPANY, a Delaware banking corporation duly organized and existing under the laws of the State of Delaware (hereinafter called the “Trustee”).

WHEREAS, The Company and the Trustee are parties to an Indenture, dated as of November 10, 2000 (the “Original Indenture”), relating to the issuance by the Company of 6% Convertible Junior Subordinated Debentures due 2030 (the “2030 Debentures”);

WHEREAS, the Company is a party to that certain Agreement and Plan of Merger with UAL Corporation and JT Merger Sub Inc., dated as of May 2, 2010 (the “Merger Agreement”), whereby, at the effective time of the transactions contemplated therein (the “Effective Time”), JT Merger Sub Inc. was merged with and into the Company, each share of the Company’s Class B common stock, par value $0.01 per share, was converted into 1.05 shares of common stock of UAL and the Company is continuing as the surviving corporation and as a wholly-owned subsidiary of UAL (collectively referred to herein as the “Merger”);

WHEREAS, the Merger constitutes a “Company Transaction” involving a “Common Stock Fundamental Change” within the meaning of Section 13.04 of the Original Indenture;

WHEREAS, the Company has duly authorized the execution and delivery of this Supplemental Indenture;

WHEREAS, the Company has requested the Trustee, and the Trustee has agreed, to join with it in the execution and delivery of this Supplemental Indenture;

WHEREAS, Section 9.01(3) of the Original Indenture provides that the Company and the Trustee, at any time and from time to time, may enter into an indenture supplemental to the Original Indenture, without the consent of any Holders of Securities, to make provision with respect to the conversion rights of Holders pursuant to the requirements of Article XIII of the Original Indenture;

WHEREAS, on the basis of the foregoing, the Trustee has determined that this Supplemental Indenture is in form satisfactory to it;

WHEREAS, the Company has furnished the Trustee with an Officers’ Certificate and an Opinion of Counsel in accordance with the requirements of Section 9.03 of the Original Indenture, stating that the execution of this Supplemental Indenture is authorized or permitted by the Original Indenture;

WHEREAS, all things necessary to make this Supplemental Indenture a valid agreement of the Company, UAL and the Trustee and a valid amendment of, and supplement to, the Original Indenture have been done. The entry into this Supplemental Indenture by the parties hereto is in all respects authorized by the provisions of the Original Indenture;

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NOW THEREFORE:

It is mutually covenanted and agreed, for the equal and proportionate benefit of all Holders of the 2030 Debentures, as follows:

ARTICLE I

RELATION TO ORIGINAL INDENTURE;

DEFINITIONS AND INCORPORATION BY REFERENCE

Section 1.1 Definitions. For all purposes of the Original Indenture and this Supplemental Indenture as they relate to the 2030 Debentures, except as otherwise expressly provided or unless the context otherwise requires:

ARTICLE II

CONVERSION INTO COMMON STOCK OF UAL

Section 2.1 Effect of Merger. From and after the Effective Time of the Merger, in accordance with Section 13.04 of the Original Indenture, the Holder of each Security then outstanding shall have the right thereafter to convert such Security only into common stock of the kind received by the holders of Class B Common Stock (as defined in the Original Indenture) in the Merger, in an amount determined pursuant to the provisions of Section 13.07(a)(ii) of the Original Indenture.

Section 2.2 Adjustments to Conversion Price. As and to the extent required by Section 13.04 of the Original Indenture, the conversion rights set forth in Article II of this Supplemental Indenture shall be subject to adjustment as a result of events occurring subsequent to the date hereof as nearly equivalent as may be practicable to the adjustments provided for in Article XIII of the Original Indenture. This Supplemental Indenture shall be deemed to constitute a “constituent document” of the Company and UAL for purposes of Section 13.04 of the Original Indenture.

Section 2.3 Affirmation. The Company hereby affirms its obligations under the Original Indenture, as supplemented by this Supplemental Indenture, including the due and punctual payment of the principal of and interest (including any Additional Payments) on all the Securities and the performance or observance of every covenant of the Original Indenture on the part of the Company to be performed or observed. UAL hereby agrees to be bound by the provisions of Section 2.1 and 2.2 of this Supplemental Indenture. For the avoidance of doubt, UAL does not assume any obligations of the Company under the Original Indenture, as supplemented and amended by this Supplemental Indenture, other than as expressly provided for in this Section 2.3. The Original Indenture, as supplemented and amended by this Supplemental Indenture, is in all respects hereby adopted, ratified and confirmed by the Company and the Trustee.

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ARTICLE III

MISCELLANEOUS

Section 3.1 Concerning the Trustee; Force Majeure. The Trustee assumes no duties, responsibilities or liabilities by reason of this Supplemental Indenture other than as set forth in the Original Indenture.

In no event shall the Trustee be responsible or liable for any failure or delay in the performance of its obligations hereunder arising out of or caused by, directly or indirectly, forces beyond its control, including, without limitation, strikes, work stoppages, accidents, acts of war or terrorism, civil or military disturbances, nuclear or natural catastrophes or acts of God, and interruptions, loss or malfunctions of utilities, communications or computer (software and hardware) services; it being understood that the Trustee shall use reasonable efforts which are consistent with accepted practices in the banking industry to resume performance as soon as practicable under the circumstances.

Section 3.2 Supplemental Indenture Controls. In the event of a conflict or inconsistency between the Original Indenture and this Supplemental Indenture, the provisions of this Supplemental Indenture shall control.

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 Multiple Originals. The parties may sign any number of copies of this Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement. One originally signed copy is enough to prove this Supplemental Indenture.

Section 3.5 Headings and Table of Contents. The Article and Section headings herein are for convenience only and shall not affect the construction hereof.

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IN WITNESS WHEREOF, the undersigned, being duly authorized, have executed this Supplemental Indenture on behalf of the respective parties hereto as of the date first above written.

CAL Signature Page

First Supplemental Indenture for 2030 Debentures

UAL Signature Page

First Supplemental Indenture for 2030 Debentures

Trustee Signature Page

First Supplemental Indenture for 2030 Debentures