AMENDMENT NO. 2 TO AMENDED AND RESTATED STOCKHOLDERS AGREEMENT

Exhibit 4.1.2

AMENDMENT NO. 2

TO

AMENDED AND RESTATED STOCKHOLDERS’ AGREEMENT

This Amendment No. 2 to Amended and Restated Stockholders’ Agreement (this “Amendment”), is made and entered into effective as of November 7, 2011, by and among Radius Health, Inc., a Delaware corporation (the “Company”), and the undersigned stockholders of the Company party to the Amended and Restated Stockholders’ Agreement, dated as of May 17, 2011, by and among the Company and the stockholders named therein (as amended, the “Agreement”).  All capitalized terms used herein and not otherwise defined herein shall have the meanings ascribed thereto in the Agreement.

WHEREAS, the Company and the undersigned parties to the Agreement, comprising the Majority Investors, desire to (i) amend the Agreement in order to specify restrictions on the sale by Stockholders of shares of the Company’s capital stock, (ii) confirm that the Company has complied with its obligations under the Agreement relating to the Registration Statement on Form S-1 (Reg. No. 333-175091) originally filed with the Commission on June 23, 2011 (as amended, the “Form S-1”), (iii) in accordance with its obligations to two option holders, grant certain registration rights under the Agreement to such individuals and (iv) permit additional holders of the Company’s securities to become parties to, and subject to, the Agreement.

NOW, THEREFORE, in consideration of the mutual promises and covenants contained herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

1.             Clause (C) of Section 3.11(b) of the Agreement is hereby amended and restated in its entirety to read as follows:

“(C) in no event shall any Stockholder be permitted, during the period commencing on the date hereof and ending on the date of the listing of the Common Stock on a national securities exchange, to sell, assign, transfer, make a short sale of, loan, grant any option for the purchase of, any shares of Common Stock for a price that is less than $8.142 per share (subject to proportionate and equitable adjustment upon any stock split, stock dividend, reverse stock split or similar event affecting the Common Stock that becomes effective after the date of this Agreement) or any other shares of capital stock of the Company for an effective price that is less than $8.142 per share on an as-converted to Common Stock basis (subject to proportionate and equitable adjustment upon any stock split, stock dividend, reverse stock split or similar event affecting the Common Stock that becomes effective after the date of this Agreement), except (x) with the prior written consent of the Company or (y) to a member of such Stockholder’s Group.”

2.             Upon, and subject to, the effectiveness of the Form S-1 on or prior to November 14, 2011, the Company shall have complied with all of its obligations under Section 3.4(a)(ii) of the Agreement with respect to the Registration Statement, no Event shall have occurred and the Company shall have no liability or obligation to pay any damages under the Agreement with

respect to such Registration Statement.  Notwithstanding the terms of Section 3.4(a)(iii), the Registrable Securities to be included in the Registration Statement shall be allocated in the manner they will have been allocated in the Form S-1.

3.             Solely of the purposes of Sections 3.4 through 3.12 of the Agreement, the shares of Common Stock issuable upon the exercise of the stock options issued to Alan H. Auerbach prior to the date hereof or upon the exercise of any stock options issued to Kurt C. Graves prior to November 30, 2011 shall be Registrable Securities as if such shares of Common Stock were Series A-1 Conversion Shares, and shall engender to each of Mr. Auerbach and Mr. Graves, as the case may be, the rights and obligations under the terms of Sections 3.4 through Section 3.12 of the Agreement (but not any other section of the Agreement) attributable to holders of Series A-1 Preferred Stock.

4.             Notwithstanding anything in the Agreement to the contrary, any holder of shares of capital stock of the Company or other securities of the Company may become a party to the Agreement following the delivery to, and written acceptance by, the Company of an executed Instrument of Adherence to the Agreement substantially in the form attached to the Agreement as Annex C.  No action or consent by Stockholder parties to the Agreement shall be required for such joinder to the Agreement by such holder, so long as such holder has agreed in writing to be bound by all of the obligations as a Stockholder party under the Agreement as indicated in the Instrument of Adherence and the Instrument of Adherence has been accepted by the Company.  Notwithstanding anything in the Agreement to the contrary, any holder of shares of capital stock of the Company or other securities of the Company may become a party to the Agreement by executing and delivering to the Company this Amendment, and no action or consent by Stockholder parties to the Agreement shall be required for such joinder to the Agreement.

5.             Each party to this Amendment that was not a party to the Agreement prior to its execution of this Amendment (an “Additional Party”) hereby agrees that such Additional Party, (i) in the case of a holder of Common Stock, has become a party and subject to the Agreement (as amended by this Amendment) in the capacity of a Common Stockholder and Stockholder, (ii) in the case of a holder of an option to purchase Common Stock, effective upon the exercise of such option, shall be a party and subject to the Agreement (as amended by this Amendment) in the capacity of a Common Stockholder and Stockholder, (iii) in the case of a holder of a warrant to purchase shares of Preferred Stock, effective upon the exercise of such warrant, shall be a party and subject to the Agreement (as amended by this Amendment) in the capacity of a Stockholder, and in each case shall be deemed to have made all of the representations and warranties made by a Stockholder under the Agreement.

6.             Except as modified by this Amendment, the Agreement is hereby reaffirmed in its entirety by the Stockholders and shall continue in full force and effect.  This Amendment shall be construed and enforced in accordance with and governed by the laws of the Commonwealth of Massachusetts, without giving effect to the principles of conflicts of laws thereof that would result in the application of the laws of any other jurisdiction.  This Amendment may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

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IN WITNESS WHEREOF, each of the undersigned has caused this Amendment to be duly executed on its behalf as of the day and year first above written.

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