Exhibit 3.4

CERTIFICATE OF AMENDMENT

OF

THE CERTIFICATE OF DESIGNATION

OF THE SERIES A PREFERRED STOCK

OF

SUNESIS PHARMACEUTICALS, INC.

SUNESIS PHARMACEUTICALS, INC., a corporation organized and existing under and by virtue of the General Corporation Law of the State of Delaware (the “Company,” or the “Corporation”), DOES HEREBY CERTIFY:

FIRST: The name of this Corporation is Sunesis Pharmaceuticals, Inc.

SECOND: The date on which the Certificate of Designation of the Series A Preferred Stock of the Corporation (the “Certificate of Designation”) was originally filed with the Secretary of State of the State of Delaware is April 3, 2009.

THIRD: Pursuant to the provisions of Section 242 of the General Corporation Law of the State of Delaware and the authority vested in the Board of Directors of the Corporation (the “Board”) by the Amended and Restated Certificate of Incorporation of the Corporation filed with the Secretary of State of the State of Delaware on September 30, 2005 (the “Restated Certificate”), the Board of Directors has duly adopted resolutions providing for the amendment of the Certificate of Designation as provided for hereunder, and such resolutions are set forth below in pertinent part:

NOW, THEREFORE, BE IT RESOLVED, that pursuant to the authority vested in the Board in accordance with the provisions of Section 242 of the General Corporation Law of the State of Delaware and the Restated Certificate, Section A(2)(b)(viii) of the Fourth Article of the Certificate of Designation shall be amended and restated to read in its entirety as follows:

“(viii) Any issuance of Common Stock (a “Common Stock Financing”); provided, however, that no consent of the Series A Preferred shall be required pursuant to this paragraph (viii) for the Common Equity Closing (as such term is defined in that certain Securities Purchase Agreement, dated March 31, 2009, by and between the Company and the other parties thereto (as amended from time to time, the “Purchase Agreement”)) and the other transactions contemplated by the Purchase Agreement; and provided, further, that no consent of the Series A Preferred shall be required under this paragraph (viii) for any Common Stock Financing that (A) provides aggregate gross cash proceeds to the Company equal to or greater than the Minimum Aggregate Common Equity Subscription Amount (as such term is defined in the Purchase Agreement) and (B) has a purchase price per share of Common Stock equal to or greater than $0.44 per share, subject to adjustment for any stock dividends, combinations, splits, recapitalizations and the like; notwithstanding the foregoing, this paragraph (viii) shall automatically terminate and be of no force or effect upon the earlier of (I) receipt by the Company of the Non-Participation Notice (as such term is defined in the Purchase Agreement), (II) January 15, 2010, if the Cash Balance Notice (as such term is defined in the Purchase Agreement) reflects a Cash (as such term is defined in the

Purchase Agreement) balance of less than $2.5 million as of January 8, 2010 and no Purchaser Put Notice (as such term is defined in the Purchase Agreement) is delivered to the Company on or before January 15, 2010, (III) December 31, 2010, if no Cash Balance Notice delivered prior to such date reflects a Cash balance less than $2.5 million, and (IV) five (5) Trading Days following the delivery to the Lead Purchasers (as such term is defined in the Purchase Agreement) of a Cash Balance Notice reflecting a Cash balance of the Company of less than $2.5 million and no Purchaser Put Notice is delivered.”; and

RESOLVED FURTHER, that, upon receipt of the requisite consent of the holders of the Series A Preferred Stock, the officers of the Company are each authorized and directed, for and on behalf of the Company, to execute this Certificate of Amendment and to file it with the Secretary of State of the State of Delaware in the form and manner as required by the laws of the State of Delaware, with such additional changes as the Secretary of State of the State of Delaware may require.

FOURTH: Pursuant to a resolution of the Board of Directors, the Amendment was submitted to the holders of the Series A Preferred Stock of the Company for their consent in accordance with the provisions of Section A(2)(b) of the Fourth Article of the Certificate of Designation, and was duly adopted.

IN WITNESS WHEREOF, Sunesis Pharmaceuticals, Inc. has caused this Certificate of Amendment to be signed by its duly authorized and elected President and Chief Executive Officer this 27th day of October, 2009.