EXHBIT 4.1

                        FORM OF 2004 A WARRANT AMENDMENT


               AMENDMENT NO. 1 TO COMMON STOCK PURCHASE WARRANT A

         This AMENDMENT NO. 1 TO COMMON STOCK PURCHASE WARRANT A dated as of
December 20, 2007 (this "Amendment"), among Geron Corporation, a Delaware
corporation (the "Company"), __________ (the "Buyer"), amends the Geron
Corporation Amended and Restated Common Stock Purchase Warrant A issued on March
13, 2007 (the "Warrant").

         WHEREAS, the Company and Holder are entering into an Agreement of even
date herewith (the "Agreement") pursuant to which the parties are agreeing,
among other things, to amend certain provisions of the Warrant; and

         WHEREAS, the Company and the Holder desire to amend certain provisions
of the Warrant, all subject to the terms, conditions and limitations set forth
herein;

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

          1.   Capitalized Terms.

         Capitalized terms used herein which are defined in the Warrant have the
same meanings herein as therein, except to the extent that such meanings are
amended hereby.

          2.   Amendment.

                  2.1. The Company and the Holder agree that the first sentence
of the Warrant is hereby deleted in its entirety and replaced with the
following:

              "THIS CERTIFIES THAT, for value received, ________ or its
              registered assigns (the "Holder"), is entitled to purchase from
              Geron Corporation, a Delaware corporation (the "Company"), at any
              time or from time to time during the period specified in Paragraph
              2 hereof, ________ (_______) fully paid and nonassessable shares
              of the Company's common stock, par value $0.001 per share (the
              "Common Stock"), at a per share exercise price equal to the lesser
              of (i) average of the closing bid prices of the Common Stock on
              the Principal Exchange (as defined in that certain Securities
              Purchase Agreement dated as of November 10, 2004, by and among the
              Company and the Buyers listed therein (the "Purchase Agreement"))
              for the five (5) Trading Day (as defined in the Purchase
              Agreement) period ending on December 15, 2009 and (ii) $7.50 (the
              "Exercise Price"); provided, however, that the Exercise Price
              shall not be less than $6.80, except as adjusted pursuant to
              Section 4 hereof."

                  2.2. The Company and the Holder agree that Paragraph 2 of the
Warrant is hereby deleted in its entirety and replaced with the following:

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              "2. Period of Exercise. This Warrant is exercisable at any time or
from time to time on or after May 11, 2005 ("Exercise Period Start Date") and
before 8:00 p.m., New York City time on November 10, 2011 (the "Exercise
Period"); provided, however, that the Exercise Period may be extended pursuant
to Section 4.13 of the Purchase Agreement."

                  2.3. The Company and the Holder agree that Paragraph 4(c) of
the Warrant is deleted in its entirety and replaced with the following:

             "Consolidation, Merger or Sale. (i) In case of (1) any
             consolidation of the Company with, or merger of the Company into
             any other corporation or entity, or (2) any sale or conveyance of
             all or substantially all of the assets of the Company other than in
             connection with a plan of complete liquidation of the Company (each
             of clause (1) and (2) shall be referred to as a "Fundamental
             Transaction"), then, as a condition of such Fundamental
             Transaction, adequate provision will be made whereby the Holder
             will thereafter (at any time or from time to time during the
             remainder of the Exercise Period) have the right to acquire and
             receive upon exercise of this Warrant in lieu of the shares of
             Common Stock immediately theretofor acquirable upon the exercise of
             this Warrant, such shares of stock, securities or assets as may be
             issued or payable with respect to or in exchange for the number of
             shares of Common Stock immediately theretofore acquirable and
             receivable upon exercise of this Warrant had such Fundamental
             Transaction not taken place.

             (ii) In any such case, the Company will make appropriate provision
             to insure that the provisions of this Paragraph 4(c) hereof will
             thereafter be applicable as nearly as may be in relation to any
             shares of stock or securities thereafter deliverable upon the
             exercise of this Warrant. The Company will not effect any
             Fundamental Transaction unless, prior to the consummation thereof,
             (1) the successor or acquiring entity (if other than the Company),
             (2) any other entity whose stock, securities or assets the holders
             of the Common Stock of the Company are entitled to receive as a
             result of such Fundamental Transaction and (3) any parent,
             subsidiary or affiliate of such successor, acquiring entity or
             other entity whose common stock this Warrant shall be exercisable
             into by virtue of subparagraph (iii) of this Paragraph 4(c) (any or
             all of such entities being hereafter referred to as a "Successor
             Entity") assumes by written instrument the obligations under this
             Paragraph 4 and the obligations to deliver to the Holder such
             shares of stock, securities or assets as, in accordance with the
             foregoing provisions, the Holder may be entitled to acquire.

             (iii) Furthermore, in the event of a transaction contemplated by
             this Paragraph 4(c) involving the acquisition of the Company by a
             Public Acquirer (as defined below) for consideration consisting of
             all or part cash, at the option of the Holder, in lieu of any cash
             in respect of shares of Common Stock underlying this Warrant, this
             Warrant (or such proportion thereof as is equal to the proportion
             of cash to stock to be paid for the Company) shall thereafter be
             exercisable for the common stock of the Public Acquirer for the
             remainder of the Exercise Period (and otherwise in accordance with
             the terms hereof), with the number of shares thereafter underlying
             this Warrant determined by multiplying the number of shares for
             which this Warrant is exercisable immediately prior to such
             transaction by a fraction, the numerator of which is the cash

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             consideration per share paid for the Company and the denominator of
             which is the Market Price of the Public Acquirer's common stock,
             where "Market Price" means the average closing price of the Public
             Acquirer's common stock over the five trading days immediately
             following the closing date of the transaction. In the case of a
             transaction involving partial cash consideration, the proportion of
             this Warrant as is equal to the proportion of stock to cash in such
             transaction shall thereafter be exercisable for stock of the Public
             Acquirer in accordance with the preceding terms of this Paragraph
             4(c), with the number of shares underlying this Warrant adjusted to
             reflect the number of shares of common stock of the Public Acquirer
             to be issued for each share of Common Stock of the Company.
             Following any adjustment hereunder, the Exercise Price shall be
             proportionately adjusted, by multiplying the Exercise Price then in
             effect by a fraction, the numerator of which is the number of
             shares issuable prior to the adjustment and the denominator of
             which is the number of shares issuable after the adjustment.
             "Public Acquirer" means any entity that has publicly traded common
             stock whether publicly traded in the United States or in any other
             jurisdiction, it being understood that (1) "common stock" as used
             in this Paragraph 4(c) includes common equity equivalents, trust
             shares, limited partnership interests, ordinary shares, American
             Depositary Receipts, American Depositary Shares, and any other
             similar securities or derivate thereof, and (2) the Company shall
             be deemed to have been acquired by a Public Acquirer where any
             Successor Entity has publicly traded common stock whether traded in
             the United States or any other jurisdiction, even if such Successor
             Entity is not the direct acquirer or successor to the Company.
             Following any transaction contemplated by this Paragraph 4(c) the
             term Warrant Shares shall be deemed to refer to the shares for
             which this Warrant is thereafter exercisable in accordance with the
             provisions hereof.

             (iv) In addition, if holders of Common Stock are given a choice as
             to the securities, cash (which shall be treated in accordance with
             the preceding paragraph) or property to be received in a
             Fundamental Transaction (including a right to elect to receive any
             particular one or combination of more than one of the foregoing),
             then the Holder shall be given the same choice of consideration
             upon any exercise of this Warrant following such Fundamental
             Transaction, which choice of consideration can be made at the time
             of exercise at any time prior to the expiration of the Exercise
             Period.

             (v) Notwithstanding the foregoing, in the event of a Fundamental
             Transaction by a Successor Entity that is not a Qualified Public
             Acquirer, the Holder may, in its sole discretion, elect to receive
             cash in exchange for this Warrant in an amount equal to the
             Theoretical Value (as defined below) of this Warrant at the time of
             the first public announcement of the Fundamental Transaction (the
             "Announcement Date"); provided, however, that the option to receive
             cash described in this subparagraph (v) shall apply only to the
             extent that the transaction is in whole or in part a cash purchase,
             and only to the extent that the holders of Common Stock are
             receiving cash, and such right to receive cash shall be pari passu
             with and not in preference to the common stockholders right to
             receive cash. In the event of a Fundamental Transaction involving a
             Successor Entity that is a Qualified Public Acquirer, at the option
             of the Holder, such Public Acquirer shall list for trading the
             Warrants, as adjusted pursuant to this Paragraph 4(c), on the AMEX,
             ICE, CBOE and regional options exchanges and quotation systems.

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             (vi) A "Qualified Public Acquirer" means a Public Acquirer that (1)
             has "common stock" publicly traded on the NYSE, NASDAQ Global
             Market, or the primary trading markets of the London Stock
             Exchange, Tokyo Stock Exchange, Euronext, Deutsche Boerse or any
             other stock exchange whose average daily U.S. dollar denominated
             trading volume (based on applicable exchange rates) is at least
             equal to lowest average daily volume of the aforementioned
             exchanges based on the trailing 12-month period ending on the
             Trading Day immediately prior to the Announcement Date.
             "Theoretical Value" means the value calculated using the Black
             Scholes valuation model, where intrinsic value, if any, is added to
             75% of the difference between full Theoretical Value and intrinsic
             value, and (1) the interest rate used will be tied to the yield of
             closest matching duration U.S. Treasury issue; and (2) the
             volatility figure used will be either (A) if the Company has listed
             options (as it currently does), the volatility associated with
             those listed options, as implied by the average price (using the
             midpoint between the bid and the ask prices) of the relevant
             options (based on closest duration and strike price) during the
             three (3) consecutive Trading Days immediately prior to the
             Announcement Date; or (B) if the Company does not have listed
             options, the thirty (30) day historical volatility of the Company's
             Common Stock calculated by Bloomberg L.P. (or a similar source
             selected by the Holder and the Company) ending on the Trading Day
             immediately prior to the Announcement Date."

          3.   Miscellaneous.

                  (a) Except as specifically amended hereby, all of the terms
and provisions of the Warrants shall remain in full force and effect.

                  (b) This Amendment may be executed in any number of
counterparts, each of which, when executed and delivered, shall be an original,
but all counterparts shall together constitute one instrument. Delivery of an
executed signature page hereto by facsimile transmission shall be effective as
delivery of a manually executed counterpart hereof. At the request of the Buyer
or any assignee, with at least ten business days advance written notice, the
Company will promptly issue an amended and restated version of the Warrant, as
amended hereby, in replacement of the Warrant, as amended hereby.

                  (c) This Amendment shall be governed by the laws of the State
of Delaware and shall be binding upon and inure to the benefit of the parties
hereto and their respective successors and assigns.

                  [Remainder of Page Left Intentionally Blank]

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         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed by their respective authorized officers as of the day and year
first above written.


                                    COMPANY:

                                    GERON CORPORATION


                                    By:
                                        ----------------------------------------
                                        Name     David J. Earp
                                        Title:   Senior Vice President, Business
                                                 Development and Chief Patent
                                                 Counsel



                                    BUYER:

                                    --------------------------------


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