Exhibit 4.1

FIRST AMENDMENT TO

SHAREHOLDER RIGHTS AGREEMENT

BETWEEN

MYREXIS, INC.

AND

AMERICAN STOCK TRANSFER & TRUST COMPANY, LLC

This First Amendment to Shareholder Rights Agreement (the “Amendment”) is made as of this 29^th day of March, 2012 by and between Myrexis, Inc. (f/k/a Myriad Pharmaceuticals, Inc.), a Delaware corporation (the “Company”), and American Stock Transfer & Trust Company, LLC, as rights agent (the “Rights Agent”). Capitalized terms used but not defined herein shall have the meanings given to such terms in the Rights Agreement (as defined below).

WHEREAS, the Company and the Rights Agent are parties to a Rights Agreement dated as of June 30, 2009 (the “Rights Agreement”);

WHEREAS, pursuant to Section 23(a) of the Rights Agreement, the Board of Directors of the Company (the “Board of Directors”) may, at its option, at any time prior to the earlier of the Stock Acquisition Date or the Final Expiration Date amend the Rights Agreement to change the Final Expiration Date to another date, including an earlier date;

WHEREAS, pursuant to Section 27 of the Rights Agreement, the Company and the Rights Agent shall, if the Company so directs, supplement or amend any provision of the Rights Agreement without the approval of any holders of shares of Common Stock of the Company;

WHEREAS, the Board of Directors desires to and has determined to amend the Rights Agreement to amend the Final Expiration Date; and

WHEREAS, all acts and things necessary to make this Amendment a valid agreement, enforceable according to its terms have been done and performed, and the execution and delivery of this Amendment by the Company and the Rights Agent have been in all respects duly authorized by the Company and the Rights Agent.

NOW, THEREFORE, in consideration of the foregoing and the mutual agreements set forth herein, the parties hereby agree as follows:

1. (a) Clause (i) of Section 7(a) of the Rights Agreement is hereby amended and restated in its entirety to read as follows:

“(i) the Close of Business on March 29, 2012 (the “Final Expiration Date”),”

(b) Consistent with the amendment to clause (i) of Section 7(a) set forth in Section(1)(a) above, Exhibit B to the Rights Agreement is hereby amended to replace the date “June 30, 2019” with the date “March 29, 2012” in the legend appearing therein.

2. This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of such State applicable to contracts to be made and performed entirely within such State.

3. This Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

4. Descriptive headings of the several Sections of this Amendment are inserted for convenience only and shall not control or affect the meaning or construction of any of the provisions hereof.

5. If any term or provision hereof or the application thereof to any circumstance shall, in any jurisdiction and to any extent, be invalid or unenforceable, such term or provision shall be ineffective as to such jurisdiction to the extent of such invalidity or unenforceability without invalidating or rendering unenforceable the remaining terms and provisions hereof or the application of such term or provision to circumstances other than those as to which it is held invalid or unenforceable.

6. This Amendment shall be effective as of the date first written above, and except as expressly amended hereby, the Rights Agreement shall remain in full force and effect and otherwise shall be otherwise unaffected hereby.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed and attested, all as of the date and year first above written.