Exhibit 3.1(c) CERTIFICATE OF AMENDMENT TO THE THIRD AMENDED AND RESTATED CERTIFICATE OF INCORPORATION OF ALLIANCE MEDICAL CORPORATION Alliance Medical Corporation, a corporation organized and existing under the General Corporation Law of Delaware ("Corporation") pursuant to Section 242 of the General Corporation Law of the State of Delaware DOES HEREBY CERTIFY AS TO THE FOLLOWING: FIRST: The name of the corporation is Alliance Medical Corporation. SECOND: The original Certificate of Incorporation was filed with the Secretary of State of the state of Delaware on October 7, 1997 under the name GB Company. On February 4, 1998, the corporation filed a Certificate of Amendment to change the name of the corporation to Alliance Medical Corporation. On August 27, 1998, the corporation filed a Certificate of Amendment to increase the authorized capital stock of the corporation. On July 12, 1999, the corporation filed a Certificate of Amendment to further increase the authorized capital stock of the corporation. On July 19, 1999, the corporation filed a Certificate of Designations, Preferences and Rights creating the Series A 8% Participating Preferred Stock of the corporation. On July 31, 2000, the corporation filed a First Amended and Restated Certificate of Incorporation creating the Series B 8% Participating Preferred Stock. On February 6, 2001, the corporation filed a Second Amended and Restated Certificate of Incorporation creating the Series C 8% Participating Preferred Stock. On August 13, 2001, the corporation filed a Third Amended and Restated Certificate of Incorporation creating the Series D 8% Participating Preferred Stock. On October 22, 2001, the corporation filed a Certificate of Amendment to effect a reverse stock split of the corporation's common stock and to insure mandatory conversion of all outstanding shares of the corporation's preferred stock upon its initial public offering of common stock. THIRD: Pursuant to Section 242(b) of the Delaware General Corporation Law (the "DGCL"), the Board of Directors of the corporation has duly adopted, and a sufficient percentage of the outstanding stock entitled to vote thereon and a sufficient percentage of the outstanding stock of each class entitled to vote as a class has approved by written consent in accordance with Section 228, the amendments to the Third Amended and Restated Certificate of Incorporation set forth in this Certificate of Amendment. FOURTH: Subsection 12 of Sections B, C, D, and E, respectively, of Article Four of the Third Amended and Restated Certificate of Incorporation are each amended to read as follows: ""Qualified Public Offering" means a firm commitment underwritten Public Offering by the Corporation of shares of its Common Stock in which (i) the aggregate price paid by the public for the shares shall be at least $30 million, and (ii) the price per share paid by the public for such shares shall be at least 300% of the Conversion Price in effect immediately prior to the closing of the sale of such shares pursuant to the Public Offering; EXCEPT THAT QUALIFIED PUBLIC OFFERING WILL HAVE THE SAME MEANING AS PUBLIC OFFERING PROVIDED THAT THE CORPORATION COMPLETES A FIRM COMMITMENT UNDERWRITTEN PUBLIC OFFERING BY MARCH 31, 2002 THAT IS APPROVED BY THE BOARD OF DIRECTORS OF THE CORPORATION." IN WITNESS WHEREOF, Alliance Medical Corporation has caused this Certificate of Amendment to be signed by the undersigned duly authorized officer this ___ day of January 2002, and the foregoing facts stated herein are true and correct. ALLIANCE MEDICAL CORPORATION By: -------------------------------------- Name: Tim Einwechter Title: Chief Financial Officer 2