<PAGE>   1

                                                       Exhibit 10.4

                             AMENDMENT NO. 3 TO THE
                           SECOND AMENDED AND RESTATED
                          REGISTRATION RIGHTS AGREEMENT


     THIS AMENDMENT NO. 3, dated as of December 9, 1996, is made to the SECOND
AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT, dated as of January 31,
1992, as previously amended by (i) Amendment No. 1 thereto, dated as of December
23, 1994, and (ii) Amendment No. 2 thereto, dated as of May 24, 1996
(collectively, the "Registration Rights Agreement"), among Creative
BioMolecules, Inc., a Delaware corporation (the "Company"), and the persons
defined as "Investors" under the Registration Rights Agreement.


                              W I T N E S S E T H:


     WHEREAS, the Company proposes to enter into a Research Collaboration and
License Agreement with Biogen, Inc. ("Biogen"), and in connection therewith to
enter into a restricted stock purchase agreement (the "Restricted Stock Purchase
Agreement") with Biogen under which Biogen will purchase from the Company a
number of shares (the "Biogen Shares") of the Company's common stock, $.01 par
value per share ("Common Stock") in an amount to be computed in accordance with
the Restricted Stock Purchase Agreement at an aggregate purchase price of
$18,000,000;

     WHEREAS, in connection with the execution of the Restricted Stock Purchase
Agreement, the Company has agreed to amend the Registration Rights Agreement to
provide certain registration rights with respect to the Biogen Shares;

     WHEREAS, the parties hereto desire to amend the Registration Rights
Agreement to, among other things, add Biogen as a party to the Registration
Rights Agreement and include the Biogen Shares as "Registrable Securities",
thereby providing to Biogen registration rights with respect to the Biogen
Shares; and

     WHEREAS, Section 17(f) of the Registration Rights Agreement provides that
terms of the Registration Rights Agreement may be amended and the observance
thereof waived with the consent of the Company and the holders of at least 50%
of the Registrable Securities (as currently defined in the Registration Rights
Agreement), and the undersigned holders of Registrable Securities collectively
hold the requisite percentage of Registrable Securities to effect this amendment
on behalf of all Investors; and

     WHEREAS, the parties believe that it is in their best interests to amend
the Registration Rights Agreement as provided herein;


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     NOW, THEREFORE, in consideration of the premises, and for other good and
valuable consideration the receipt of which is hereby acknowledged, the parties
hereto agree as follows:

     1.   To amend the Registration Rights Agreement as follows:

          (a)  Biogen shall be included within the definition of "Investors" in
               the Registration Rights Agreement and shall have the same rights
               and privileges as apply to the existing Investors thereunder,
               PROVIDED THAT Biogen executes an instrument of adherence to
               the Registration Rights Agreement bearing the address to be used
               for notice under the Registration Rights Agreement.

          (b)  The definition of Registrable Securities in Section 2(b) of the
               Registration Rights Agreement shall be amended to include the
               Biogen Shares and any shares of Common Stock subsequently issued
               to Biogen with respect to the Biogen Shares.

     2.   Except as otherwise expressly provided herein, the Registration Rights
          Agreement is hereby ratified and confirmed and shall remain in full
          force and effect.


     IN WITNESS WHEREOF, the parties hereto have caused this AMENDMENT NO. 3 TO
THE SECOND AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT to be executed as
an instrument under seal as of the date first written above.


                                CREATIVE BIOMOLECULES, INC.



                                By:  /s/ Wayne E. Mayhew III
                                    -----------------------------------
                                Name:   Wayne E. Mayhew III
                                Title:  Vice President and
                                        Chief Financial Officer


                                THE INVESTORS

                                Name of Investor: APA Excelsior Venture
                                                  Capital Holdings
                                                  (Jersey) Limited

                                By:  /s/ Alan Patricof
                                    -----------------------------------

                                Title: Patricof & Co. Ventures, Inc.
                                       Investment Manager


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                                Name of Investor: Apax CR II(A)


                                By:  /s/ Maurice Tchenio
                                    -----------------------------------
                                Title:  PDG
                                      ---------------------------------



                                Name of Investor: Apax CR II(C)


                                By:  /s/ Maurice Tchenio
                                    -----------------------------------
                                Title:  PDG
                                      ---------------------------------


                                Name of Investor: MMG Conseil


                                By:  /s/ Maurice Tchenio
                                    -----------------------------------
                                Title:  PDG



                                Name of Investor: Apax Venture
                                                  Capital Fund Ltd.


                                By:  /s/ Coutts (Jersey) Limited
                                    -----------------------------------


                                Name of Investor: Apax Ventures II, Ltd.


                                By:  /s/ Coutts (Jersey) Limited
                                    -----------------------------------


                                Name of Investor: Apax Ventures III


                                By:  /s/ Apax Funds Nominee Ltd.
                                    -----------------------------------


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                                Name of Investor: Apax Ventures III
                                                  International
                                                  Partners, L.P.


                                By:  /s/ Apax Funds Nominee Ltd.
                                    -----------------------------------


                                Name of Investor: Apax Ventures IV


                                By:  /s/ Apax Funds Nominee Ltd.
                                    -----------------------------------


                                Name of Investor: Apax Ventures IV
                                                  International
                                                  Partners, L.P.


                                By:  /s/ Apax Funds Nominee Ltd.
                                    -----------------------------------


                                Name of Investor: Biotechnology
                                                  Investments Limited


                                By:  /s/ T. Fowler         /s/ H. Casey
                                    -----------------------------------
                                Title:  Authorized Signatories
                                      ---------------------------------



                                Name of Investor: Charles Cohen


                                By:  /s/ Charles Cohen
                                    -----------------------------------
                                Title:  Chief Scientific Officer
                                      ---------------------------------


                                Name of Investor: Domain Partners III, LP

                                      One Palmer Square Associates III, LP
                                By:  /s/ Kathleen K. Schoemaker
                                    -----------------------------------
                                Title:  General Partner
                                      ---------------------------------

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                                Name of Investor: DP III Associates, LP

                                      One Palmer Square Associates III, LP
                                By:  /s/ Kathleen K. Schoemaker
                                    -----------------------------------
                                Title:  General Partner
                                      ---------------------------------


                                Name of Investor: Arthur J. Hale, M.D.


                                By:  /s/ Arthur J. Hale
                                    -----------------------------------
                                Title:  Director
                                      ---------------------------------


                                Name of Investor: PruTech
                                                  Research & Development
                                                  Partnership III


                                     R&D Funding Corp. General Partner
                                By:  /s/ Patrick Owen Burns
                                    -----------------------------------
                                Title:  Vice President
                                      ---------------------------------


                                Name of Investor: Jeffrey Wiesen


                                By:  /s/ Jeffrey M. Wiesen
                                    -----------------------------------