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                                                                     EXHIBIT 3.2



                            CERTIFICATE OF AMENDMENT
                                       OF
                      RESTATED CERTIFICATE OF INCORPORATION
                                       OF
                                GERON CORPORATION

Thomas B. Okarma and David L. Greenwood hereby certify that:

        FIRST: They are the duly elected and acting President and Secretary of
Geron Corporation, a Delaware corporation.

        SECOND: The name of this Corporation is Geron Corporation (the
"Corporation").

        THIRD: The date on which the Restated Certificate of Incorporation as
filed with the Secretary of State of the State of Delaware (the "Secretary of
State") is March 24, 1998. The date on which the Certificate of Designation was
filed with the Secretary of State is March 27, 1998.

        FOURTH: The amendment to the Corporation's Amended and Restated
Certificate of Incorporation set forth below was duly adopted by the Board of
Directors of the Corporation, and approved by the Stockholders in accordance
with the provisions of Section 242 of the General Corporation Law of the State
of Delaware.

        FIFTH: Article IV, Paragraph (A) of the Corporation's Restated
Certificate of Incorporation is amended to read in its entirety as follows:

               "(A) Class of Stock. The Corporation is authorized to issue two
        classes of stock to be designated, respectively, "Common Stock" and
        "Preferred Stock." The total number of shares which the Corporation is
        authorized to issue is Thirty-Eight Million (38,000,000) shares.
        Thirty-Five Million (35,000,000) shares shall be Common Stock, par value
        $0.001 per share and Three Million (3,000,000) shares shall be Preferred
        Stock, par value $0.001 per share.

        IN WITNESS WHEREOF, the undersigned have signed this Certificate of
Amendment of Restated Certificate of Incorporation this 10th day of December,
1999 and hereby affirm and acknowledge under the penalty of perjury that the
filing of this Certificate of Amendment of Amended and Restated Certificate of
Incorporation of Geron Corporation is the act and deed of Geron Corporation.

                                            GERON CORPORATION

                                            By:    /s/  Thomas B. Okarma
                                               ---------------------------------
                                                   Thomas B. Okarma, President

Attest:

By:   /s/ David L. Greenwood
   ---------------------------------
      David L. Greenwood, Secretary