Exhibit 10.4

THIS WARRANT AND THE SHARES ISSUABLE HEREUNDER HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY STATE SECURITIES LAWS, AND MAY NOT BE SOLD, PLEDGED, OR OTHERWISE TRANSFERRED WITHOUT AN EFFECTIVE REGISTRATION THEREOF UNDER SUCH ACT AND LAWS OR PURSUANT TO RULE 144 AND EXEMPTIONS UNDER APPLICABLE STATE SECURITIES LAWS, OR, SUBJECT TO SECTION 5.3 HEREOF, AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE COMPANY AND ITS COUNSEL, THAT SUCH REGISTRATION IS NOT REQUIRED.

WARRANT TO PURCHASE SERIES A-1 CONVERTIBLE PREFERRED STOCK

Issuer:  Radius Health, Inc.
Number of Shares:  818
Class of Stock: Series A-1 Convertible Preferred Stock, par value $.0001 per share
Exercise Price:  $81.42 per share, subject to adjustment
Issue Date:  December 14, 2011
Expiration Date: December 14, 2016

FOR THE AGREED UPON VALUE of $1.00, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, this Warrant is issued to LEERINK SWANN LLC (together with its successors and permitted assigns, “Holder”) by RADIUS HEALTH, INC., a Delaware corporation (the “Company”).

Subject to the terms and conditions hereinafter set forth, the Holder is entitled upon surrender of this Warrant and a duly executed Notice of Exercise in substantially the form attached hereto as Appendix 1 (the “Notice of Exercise”), at the principal office of the Company, 201 Broadway, 6th Floor, Cambridge, Massachusetts 02139, or such other office as the Company shall notify the Holder of in writing, to purchase from the Company up to eight hundred eighteen (818) of fully paid and non-assessable shares (the “Shares”) of the Company’s Series A-1 Convertible Preferred Stock, $.0001 par value per share (the “Class”), at a purchase price per Share of eighty one dollars and 42/100 ($81.42) (the “Exercise Price”).  Subject to the terms and conditions hereinafter set forth, this Warrant may be exercised in whole or in part at any time and from time to time until 5:00 PM, Eastern time, on the Expiration Date set forth above, and shall be void thereafter.  Until such time as this Warrant is exercised in full or expires, the Exercise Price and the number of Shares are subject to adjustment from time to time as hereinafter provided.  This Warrant is issued in connection with that certain letter agreement dated September 24, 2010 by and between the Company and the Holder (the “Agreement”).  Capitalized terms used and not otherwise defined herein shall have the respective meanings set forth in the Agreement.

Notwithstanding the foregoing definition of Class, upon and after the automatic or voluntary conversion, redemption or retirement of all (but not less than all) of the outstanding shares of such Class, including without limitation the Company’s initial registered underwritten public offering and sale of its securities (“IPO”), then from and after the date upon which all such outstanding shares have been so converted, redeemed or retired, “Class” shall mean the Company’s common stock, $.0001 par value per share (“Common Stock”), and this Warrant shall be exercisable for such number of shares of Common Stock as shall equal the number of shares of Common Stock into which the Shares would have been converted pursuant to the Company’s Certificate of Incorporation, as amended from time to time, including without limitation the Certificate of Designations, if any, applicable to the same class or series of preferred stock as the Shares (the “Certificate”) had the Shares been issued and outstanding immediately prior to such conversion, redemption or retirement, and the Exercise Price shall be the Common Stock conversion price as determined pursuant to the Certificate immediately prior to such conversion, redemption or retirement (all subject to further adjustment as provided herein).

ARTICLE 1.  EXERCISE.

1.1           Method of Exercise.  The Holder may exercise this Warrant by delivering this Warrant together with a duly executed Notice of Exercise to the principal office of the Company.  Unless the Holder is exercising the conversion right set forth in Section 1.2, the Holder shall also deliver to the Company a check for the aggregate Exercise Price for the Shares being purchased.

1.2           Conversion Right.  In lieu of exercising this Warrant as specified in Section 1.1, the Holder may from time to time convert this Warrant, in whole or in part, into a number of Shares determined as follows:

X = Y (A-B)/A

where:

X = the number of Shares to be issued to the Holder.

Y = the number of Shares with respect to which this Warrant is being exercised.

A = the Fair Market Value (as determined pursuant to Section 1.3 below) of one Share.

B = the Exercise Price.

1.3           Fair Market Value.

1.3.1        If the Company’s Common Stock is traded in a public market on a nationally recognized securities exchange or over the counter market and the Shares are

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Common Stock, the fair market value of each Share shall be the closing price of a Share reported for the business day immediately preceding the date of Holder’s Notice of Exercise to the Company (or in the instance where the Warrant is exercised immediately prior to the effectiveness of the Company’s initial public offering, the “price to public” per share price specified in the final prospectus relating to such offering).  If the Company’s Common Stock is traded in a public market on a nationally recognized securities exchange or over the counter market and the Shares are preferred stock, the fair market value of a Share shall be the closing price of a share of the Company’s Common Stock reported for the business day immediately  preceding the date of Holder’s Notice of Exercise to the Company (or in the instance where the Warrant is exercised immediately prior to the effectiveness of the Company’s initial public offering, the initial “price to public” per share price specified in a final prospectus relating to such offering), in both cases, multiplied by the number of shares of the Company’s Common Stock into which a Share is convertible.

1.3.2        If shares of the Class (or shares of the Company’s stock into which shares of the Class are convertible or exchangeable) are not traded on a nationally recognized securities exchange or over the counter market, the Board of Directors of the Company shall determine fair market value in its reasonable good faith judgment.

1.4           Delivery of Certificate and New Warrant.  Promptly after Holder exercises or converts this Warrant, the Company at its sole expense shall promptly deliver to Holder (i) certificates for the Shares acquired upon such exercise, and (ii) if this Warrant has not been fully exercised or converted and has not expired, a new warrant of like tenor representing the Shares for which this Warrant is still exercisable.

1.5           Replacement of Warrants.  On receipt of evidence reasonably satisfactory to the Company of the loss, theft, destruction or mutilation of this Warrant and, in the case of loss, theft or destruction, on delivery of an indemnity agreement reasonably satisfactory in form and amount to the Company or, in the case of mutilation, on surrender and cancellation of this Warrant, the Company at its expense shall execute and deliver, in lieu of this Warrant, a new warrant of like tenor.

1.6           Assumption/Repurchase on Sale, Merger, or Consolidation of the Company.

1.6.1        “Acquisition”.  For the purpose of this Warrant, “Acquisition” means any sale, assignment, transfer, exclusive license, or other disposition of all or substantially all of the assets of the Company, or any acquisition, reorganization, consolidation, or merger of the Company where the holders of the Company’s outstanding voting equity securities immediately prior to the transaction (i) receive cash, stock, securities or other property in respect of or in exchange for such voting equity securities pursuant to any of the transactions referred to in the foregoing provisions of this Section 1.6.1, and (ii) in the event that such transaction consists of any acquisition, reorganization, consolidation or merger of the Company, beneficially own less than a majority of the outstanding voting equity securities of the surviving or successor entity immediately following the transaction.

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1.6.2        Assumption of Warrant.  Upon the closing of any Acquisition (other than an Acquisition in which the consideration received by the Company’s stockholders consists solely of cash, debt securities or a combination of cash and debt securities), and as a condition precedent thereto, the successor or surviving entity shall assume the obligations of this Warrant, and this Warrant shall be exercisable for the same securities and property as would be payable for the Shares issuable upon exercise of the unexercised portion of this Warrant as if such Shares were outstanding on the record date for the Acquisition and subsequent closing.  The Exercise Price shall be adjusted accordingly, and the Exercise Price and number and class of Shares shall continue to be subject to adjustment from time to time in accordance with the provisions hereof.

1.6.3        Purchase Right.  Notwithstanding the foregoing, upon the closing of any Acquisition in which the consideration paid to the Company or stockholders is cash or cash equivalents, at the election of Holder, the Company shall purchase the unexercised portion of this Warrant for cash for an amount equal to (a) the fair market value of any consideration that would have been received by Holder in consideration for the Shares had Holder exercised the unexercised portion of this Warrant immediately before the record date for determining the shareholders entitled to participate in the proceeds of the Acquisition, less (b) the aggregate Exercise Price of the Shares, but in no event less than zero.

ARTICLE 2.  ADJUSTMENTS TO THE SHARES.

2.1           Dividends, Splits, Etc.   If the Company declares or pays a dividend on the outstanding shares of the Class, payable in Common Stock, other securities or any type of property, or subdivides the outstanding shares of the Class into a greater number of shares of the Class, or subdivides the shares of the Class in a transaction that increases the amount of Common Stock into which such shares are convertible, then upon exercise of this Warrant, for each Share acquired, Holder shall receive, without additional cost to Holder, the total number and kind of securities or property to which Holder would have been entitled had Holder owned the Shares of record as of the date the dividend or subdivision occurred.

2.2           Reclassification, Exchange or Substitution.  Upon any reclassification, exchange, substitution, reorganization or other event that results in a change of the number and/or class of the securities issuable upon exercise or conversion of this Warrant, Holder shall be entitled to receive, upon exercise or conversion of this Warrant, the number and kind of securities and property that Holder would have received for the Shares if this Warrant had been exercised immediately before such reclassification, exchange, substitution, reorganization or other event.  The Company or its successor shall promptly issue to Holder a new warrant of like tenor for such new securities or other property.  The new warrant shall provide for adjustments which shall be as nearly equivalent as may be practicable to the adjustments provided for in this Article 2 including, without limitation, adjustments to the Exercise Price and to the number of securities or property issuable upon exercise of the new warrant.  The provisions of this Section 2.2 shall similarly apply to successive reclassifications, exchanges, substitutions, reorganizations or other events.

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2.3           Adjustments for Combinations, Etc.  If the outstanding shares of the Class are combined or consolidated, by reclassification or otherwise, into a lesser number of shares, the Exercise Price shall be proportionately increased and the number of Shares issuable upon exercise or conversion of this Warrant shall be proportionately decreased.

2.4           No Impairment.  The Company shall not, by amendment of the Certificate or its by-laws or through a reorganization, transfer of assets, consolidation, merger, dissolution, issue, or sale of securities or any other voluntary action, avoid or seek to avoid the observance or performance of any of the terms to be observed or performed under this Warrant by the Company, but shall at all times in good faith assist in carrying out of all the provisions of this Article 2 and in taking all such action as may be necessary or appropriate to protect Holder’s rights under this Article against impairment.

2.5           Adjustments for Dilutive Issuances.  The Conversion Price (as defined in the Certificate) with respect to the Class is subject to adjustment for Dilutive Issuances (as defined in the Certificate) in accordance with Section 7(e)(i) of Part A of Article III of the Certificate.

2.6           Fractional Shares.  No fractional Shares shall be issuable upon exercise or conversion of the Warrant and the number of Shares to be issued shall be rounded down to the nearest whole Share.  If a fractional Share interest arises upon any exercise or conversion of this Warrant, the Company shall eliminate such fractional Share interest by paying Holder an amount computed by multiplying such fractional interest by the Fair Market Value (determined in accordance with Section 1.3 above) of one Share.

2.7           Certificate as to Adjustments.  Upon each adjustment of the Exercise Price, number or class of Shares or number of shares of Common Stock or other securities for which the Shares are convertible or exchangeable, the Company at its expense shall promptly compute such adjustment, and furnish Holder with a certificate of its chief financial officer setting forth such adjustment and the facts upon which such adjustment is based.  The Company shall at any time and from time to time, upon written request, furnish Holder with a certificate setting forth the Exercise Price, number and class of Shares and conversion ratio in effect upon the date thereof and the series of adjustments leading to such Exercise Price, number and class of Shares and conversion ratio.

ARTICLE 3.  COVENANTS OF THE COMPANY.

3.1           Notice of Certain Events.  If the Company proposes at any time (a) to declare any dividend or distribution upon any of  its capital stock, whether in cash, property, stock, or other securities and whether or not a regular cash dividend; (b) to offer for subscription pro rata to the holders of any class or series of its stock any additional shares of stock of any class or series or other rights; (c) to effect any reclassification or recapitalization of any of its securities; (d) to merge or consolidate with or into any other corporation, or sell, lease, license, or convey all or substantially all of its assets, or to liquidate, dissolve or wind up; or (e) offer holders of registration rights the opportunity to participate in an underwritten public offering of the

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Company’s securities for cash, then, in connection with each such event, the Company shall give Holder (1) at least 20 days prior written notice of the date on which a record will be taken for such dividend, distribution, or subscription rights (and specifying the date on which the holders of securities of the Company shall be entitled to receive such dividend, distribution or rights) or for determining rights to vote, if any, in respect of the matters referred to in (c) and (d) above; (2) in the case of the matters referred to in (c) and (d) above at least 20 days prior written notice of the date when the same will take place (and specifying the date on which the holders of securities of the Company will be entitled to exchange their securities of the Company for securities or other property deliverable upon the occurrence of such event); and (3) in the case of the matter referred to in (e) above, the same notice as is given to the holders of such registration rights.

ARTICLE 4.  REPRESENTATIONS OF THE HOLDER

4.1           Purchase for Investment.  The Holder represents and warrants that it is acquiring the Warrant, and upon exercise will hold the Shares, solely for its account for investment and not with a view to or for sale or distribution of said Warrant or Shares in violation of the Securities Act.  The Holder also represents that the entire legal and beneficial interests of the Warrant and Shares the Holder is acquiring is being acquired for, and will be held for, its account only.

4.2           Securities Not Registered.  The Holder understands that the Warrant has not been registered under the Securities Act on the basis that no distribution or public offering of the stock of the Company is to be effected.  The Holder realizes that the basis for the exemption may not be present if, notwithstanding its representations, it has in mind merely acquiring the securities for a fixed or determinable period in the future, or for a market rise, or for sale if the market does not rise.  The Holder has no such intention.

4.3           Securities to be Held Indefinitely.  The Holder recognizes that the Warrant and Shares being acquired by it must be held indefinitely unless they are subsequently registered under the Securities Act or an exemption from such registration is available.  The Holder recognizes that except as expressly set forth herein, the Company has no obligation to register the Warrant or to comply with any exemption from such registration.

4.4           Rule 144.  The Holder is aware that neither the Warrant nor the Shares may be sold pursuant to Rule 144 adopted under the Securities Act unless certain conditions are met and until the Holder has held the Shares for at least one year.

ARTICLE 5.  MISCELLANEOUS.

5.1           Automatic Conversion upon Expiration.  In the event that, upon the Expiration  Date, the Fair Market Value of one Share (or other security issuable upon the exercise hereof) as determined in accordance with Section 1.3 above is greater than the Exercise Price in effect on such date, then this Warrant shall automatically be deemed on and as of such date to be converted pursuant to Section 1.2 above as to all Shares (or such other securities) for which it

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shall not previously have been exercised or converted, and the Company shall promptly deliver a certificate representing the Shares (or such other securities) issued upon such conversion to the Holder.

5.2           Legends.  This Warrant and the Shares (and the securities issuable, directly or indirectly, upon conversion of the Shares, if any) shall be imprinted with a legend in substantially the following form:

THIS SECURITY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY STATE SECURITIES LAWS, AND MAY NOT BE SOLD, PLEDGED OR OTHERWISE TRANSFERRED WITHOUT AN EFFECTIVE REGISTRATION THEREOF UNDER SUCH ACT AND LAWS OR PURSUANT TO RULE 144 AND EXEMPTIONS UNDER APPLICABLE STATE SECURITIES LAW, OR, SUBJECT TO SECTION 5.3 OF THAT CERTAIN WARRANT TO PURCHASE STOCK ISSUED BY THE COMPANY TO LEERINK SWAN LLC DATED AS OF MAY 17, 2011, AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE COMPANY AND ITS COUNSEL THAT SUCH REGISTRATION IS NOT REQUIRED.

5.3           Compliance with Securities Laws on Transfer.  This Warrant and the Shares (and the securities, if any, issued and issuable, upon conversion of the Shares, if any) may not be transferred or assigned in whole or in part without compliance with applicable federal and state securities laws by the transferor and the transferee (including, without limitation, the delivery of investment representation letters and legal opinions reasonably satisfactory to the Company, as reasonably requested by the Company).  The Company shall not require Holder to provide an opinion of counsel if the transfer is to an affiliate of Holder, or if (a) there is no material question as to the availability of current information as referenced in Rule 144(c), (b) Holder represents that it has complied with Rule 144(d) and (e) in reasonable detail, (c) the selling broker represents that it has complied with Rule 144(f), and (d) the Company is provided with a copy of Holder’s notice of proposed sale.

5.4           Transfer Procedure.  Following its receipt of this executed Warrant, Holder may, subject to Section 5.3 above and the last sentence of this Section 5.4, transfer all or part of this Warrant and/or the Shares (or the securities, if any, issued and issuable upon conversion of the Shares) at any time and from time to time by giving the Company notice of the portion of the Warrant and/or Shares (or the securities, if any, issued and issuable upon conversion of the Shares) being transferred setting forth the name, address and taxpayer identification number of the transferee and surrendering this Warrant to the Company for reissuance to the transferee(s) (and Holder if applicable); provided, that at all times prior to the Company’s IPO, Holder shall not, without the prior written consent of the Company, transfer this Warrant (or any part hereof), any Shares, or any securities issued or issuable upon conversion of the Shares, to any person who directly competes with the Company, unless such transfer is in connection with an Acquisition of

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the Company by any such person or the stock of the transferee is publicly traded.  Any transferee (including, without limitation, any affiliate of Holder) shall execute and deliver an Instrument of Adherence, in the form attached as Appendix 2 hereto (an “Instrument of Adherence”), to that certain Amended and Restated Stockholders’ Agreement, dated as of May 17, 2011, by and among the Company and the stockholder parties thereto, as amended from time to time.

5.5           Effect of Violation of Transfer Restrictions; Preventive Measures.  Any offer, sale, assignment, transfer, endorsement, pledge, mortgage, hypothecation, or other conveyance or disposition of all or any portion of this Warrant or any Shares issued from time to time upon exercise of this Warrant, or of any interest in this Warrant or any of such Shares, in violation of this Section 5 shall be null and void.  The Company may make a notation on its records or give instructions to any of its transfer agents in order to implement the restrictions on transfer set forth in this Section 5.

5.6           Warrant Binding Upon Assignee or Successor.  The terms and conditions of this Warrant shall be binding upon any permitted assignee and successor of the Holder.  Any such successor or assignee shall be obligated to and shall immediately execute an instrument which provides that such party is bound under the terms of this Warrant.  Any transfer, assignment or other disposition without such execution by the proposed transferee, assignee or successor shall be null and void.

5.7           No Rights as Stockholder.  The Holder shall not be entitled to vote or to receive dividends or to be deemed the holder of shares of the Company’s capital stock that may at any time be issuable upon exercise of this Warrant for any purpose whatsoever, nor shall anything contained herein be construed to confer upon the Holder any of the rights of a stockholder of the Company or any right to vote for the election of directors or upon any matter submitted to stockholders at any meeting thereof, or to give or withhold consent to any corporate action (whether upon any recapitalization, issuance or reclassification of stock, change of par value or change of stock to no par value, consolidation, merger or conveyance or otherwise), or to receive notice of meetings, or to receive dividends or subscription rights, until the Holder shall have exercised the Warrant and shall have been issued Shares in accordance with the provisions hereof.

5.8           Notices.  All notices and other communications from the Company to the Holder, or vice versa, shall be deemed delivered and effective when given personally, or mailed by first-class registered or certified mail, postage prepaid, or sent via reputable overnight courier service, fee prepaid, at such address as may have been furnished to the Company or the Holder, as the case may be, in writing by the Company or such holder from time to time, but in all cases, unless instructed in writing otherwise, the Company shall deliver a copy of all notices to Holder to Leerink Swann LLC, One Federal Street, 37th Floor, Boston, Massachusetts 02110, Attention Donald D. Notman, Jr.

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5.9           Waiver.  This Warrant and any term hereof may be changed, waived, discharged or terminated only by an instrument in writing signed by the party against which enforcement of such change, waiver, discharge or termination is sought.

5.10         Attorneys Fees.  In the event of any dispute between the parties concerning the terms and provisions of this Warrant, the party prevailing in such dispute shall be entitled to collect from the other party all costs incurred in such dispute, including reasonable attorneys’ fees.

5.11         Survival of Representations, Warranties and Agreements.  All representations and warranties of the Company contained herein shall survive the date of this Warrant, the exercise or conversion of this Warrant (or any part hereof) and/or the termination or expiration of rights hereunder.  All agreements of the Company contained herein shall survive indefinitely until, by their respective terms, they are no longer operative.  The obligations of the Holder (and/or of any transferee of the Warrant or any Shares issued from time to time upon exercise of this Warrant) shall, with respect to any Shares issued upon exercise of this Warrant, survive the exercise, expiration or other termination, or transfer, of this Warrant indefinitely.

5.12         Counterparts.  This Warrant may be executed in counterparts, all of which together shall constitute one and the same agreement.

5.13         Governing Law.  This Warrant shall be governed by and construed in accordance with the laws of The Commonwealth of Massachusetts, without giving effect to its principles regarding conflicts of law.

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IN WITNESS WHEREOF, the Company has caused this Warrant to Purchase Series A-1 Convertible Preferred Stock to be executed as an instrument under seal by its duly authorized representative as of the date first above written.

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APPENDIX 1

NOTICE OF EXERCISE

1.             The undersigned hereby elects to purchase               shares of the                          stock of                                      pursuant to Section 1.1 of the attached Warrant, and tenders herewith payment of the Exercise Price of such shares in full.

1.             The undersigned hereby elects to convert the attached Warrant into Shares in the manner specified in Section 1.2 of the attached Warrant.  This conversion is exercised with respect to                          of shares of the                                                  Stock of                                       .

[Strike paragraph that does not apply.]

2.             Please issue a certificate or certificates representing said Shares in the name of the undersigned or in such other name as is specified below:

3.             The undersigned represents it is acquiring the Shares solely for its own account and not as a nominee for any other party and not with a view toward the resale or distribution thereof except in compliance with applicable securities laws.

APPENDIX 2

Instrument of Adherence to
Amended and Restated
Stockholders’ Agreement
dated May 17, 2011

                            , 20     

Reference is hereby made to that certain AMENDED AND RESTATED STOCKHOLDERS’ AGREEMENT, dated the 17th day of May, 2011, entered into by and among Radius Health, Inc., a Delaware corporation (the “Corporation”), and the Stockholder parties thereto, as amended from time to time (the “Agreement”). Capitalized terms used herein without definition shall have the respective meanings ascribed thereto in the Agreement.

The undersigned (the “New Stockholder Party”), in order to become the owner or holder of up to 818 shares of Series A-1 Preferred Stock issuable upon exercise of that certain Warrant to Purchase Series A-1 Convertible Preferred Stock, dated December 14, 2011, held by the undersigned as of the date hereof (the “Warrant”) and all other shares of the Corporation’s capital stock hereinafter acquired, hereby agrees that, from and after the date of exercise of the Warrant and the resulting issuance by the Corporation of any shares of Series A-1 Preferred Stock (or shares of Common Stock issuable upon conversion of such shares of Series A-1 Preferred Stock) to the New Stockholder Party, the undersigned has become a Stockholder party to the Agreement in the capacity of a Stockholder, and is entitled to all of the benefits under, and is subject to all of the obligations, restrictions and limitations set forth in, the Agreement that are applicable to such Stockholder parties and shall be deemed to have made all of the representations and warranties made by such Stockholder parties thereunder.  This Instrument of Adherence shall take effect and shall become a part of the Agreement on the latest date of execution by both the New Stockholder Party and the Corporation.

Executed as of the date set forth above.