<PAGE>

[Confidential Treatment Requested. Confidential Portions of this Agreement
have been redacted and filed separately with the Commission.]


                                                                    EXHIBIT 10.4


                                                            EXECUTION COPY
                      FIRST AMENDMENT OF LICENSE AGREEMENT

     This First Amendment of License Agreement is made and effective as of 25
September 2000, by and between Becton, Dickinson and Company, a New Jersey
corporation through its BD Biosciences Division, having a place of business at 7
Loveton Circle, Sparks, Maryland 21152 (hereinafter "Becton") and Nanogen, Inc.,
a Delaware corporation having its principal office and place of business at
10398 Pacific Center Court, San Diego, California 92121 (hereinafter "Nanogen").

     WHEREAS, Becton and Nanogen are parties to a certain License Agreement
effective 1 October 1997 (hereinafter "LA"); and

     WHEREAS, the parties desire to amend certain provisions of the LA.

     NOW, THEREFORE, for good and valuable consideration, the parties hereby
agree to amend the LA as follows:

     1.   Paragraph 1.5 is hereby amended to read in its entirety as follows:

          1.5  "Field" shall mean (a) IN VITRO human genetic testing, (b) IN
               VITRO human cancer diagnostics, (c) IN VITRO testing of
               agricultural samples, (d) IN VITRO testing of environmental
               samples, (e) IN VITRO testing of veterinary samples and (f)
               biomedical research applications not required to be reviewed or
               approved by the U.S. Food and Drug Administration or a foreign
               equivalent government organization, all of (a) through (f)
               employing electronically addressable oligonucleotide arrays.

     2.   Paragraph 1.8 is hereby amended by adding after the words "Licensed
          Products by Nanogen" the words "in the Field".

     3.   Paragraph 1.11 is hereby amended to read in its entirety as follows:

          1.11 "Research Agreement" shall mean the Collaborative Research and
               Development and License Agreement entered into by Becton, Nanogen
               and the Partnership as of October 1, 1997, as amended as of
               September 25, 2000.

     4.   Paragraph 1.12 is hereby amended by adding after "on behalf of
          Nanogen" the words "or by a sublicensee of Nanogen."

     5.   Paragraph 2.2 is hereby amended to read in its entirety as follows:

          2.2.1 Sublicensing

<PAGE>

               (a)         Nanogen may grant sublicenses in and to the rights
                           licensed hereunder, provided that such sublicenses
                           are in full compliance with all of the provisions set
                           forth in this Section 2.2.

               (b)         No more than five (5) business days after execution
                           of any sublicense agreement pursuant to Paragraph
                           2.2(a), Nanogen shall deliver to Becton a complete
                           and accurate copy of such sublicense agreement.

               (c)         Nanogen shall pay to Becton **********************
                           *********************************** actually paid to
                           Nanogen from sublicensees. Nanogen shall also pay to
                           BD **********************************************
                           *****************************************************
                           unless permitted by Section 4.0 or Section 8.0.

               (d)         All sublicense agreements shall require the
                           sublicensee to comply with all the terms and
                           conditions of this Agreement applicable to Nanogen,
                           provided, however that, such sublicense agreements
                           shall not include grants of rights to the sublicensee
                           to: (a) have made Licensed Products; or (b) grant
                           further sublicenses (except by implication through
                           sale of Licensed Products to end-users of such
                           products).

               (e)         All other terms and conditions of any sublicense
                           agreement shall be consistent with the terms and
                           conditions of this Agreement.

          6. Paragraph 3.1 is hereby amended to add the following sentence at
             the end of the paragraph:

                           If Nanogen or its Affiliates sell Licensed Products
                           to or through a distributor, ***********************
                           ****************************************************
                           ****************************************************
                           ****************

           7.  Paragraph 8 is hereby amended as follows:

                           Paragraph 8.1 is hereby amended by adding after the
                           words "that Nanogen's" the words "or to Nanogen's
                           knowledge, a sublicensee's".

                           Paragraph 8.2 is hereby amended by adding in the last
                           line after the words "action instituted against
                           Nanogen" the words "or a sublicensee".

                           Paragraph 8.3 is hereby amended by adding in the last
                           line after the words "proposed settlement by Nanogen"
                           the words "or a sublicensee".

                           Paragraph 8.4 is hereby amended by adding in the
                           second line after the words "split evenly by Nanogen
                           and Becton" the words "or the sublicensee and Becton
                           as applicable," and in the last line after the words
                           "and paid by, Nanogen" the words "or the sublicensee,
                           as applicable".



------------------
*** Confidential material redacted and separately filed with the Commission.


<PAGE>

                           Paragraph 8.5 is hereby amended by adding in the
                           second line after the words "8.2, Nanogen" the words
                           "or the sublicensee," in the third line after the
                           words "action, Nanogen" the words "or the
                           sublicensee," and in the fifth line after the words
                           "then Nanogen" the words "or the sublicensee".

                           Paragraph 8.6 is hereby amended by adding in the
                           beginning of the second line after the words "action,
                           Nanogen" the words "or the sublicensee" and in the
                           end of the second line after the words "which
                           Nanogen" the words "or the sublicensee".

          8.   Appendix A is hereby amended, and the First Revised Appendix A is
               attached hereto.


     IN WITNESS WHEREOF, the parties have executed this First Amendment of
License Agreement through duly authorized representatives on the dates set forth
below, effective as of the date first written above.

NANOGEN, INC.                               BECTON, DICKINSON AND COMPANY
                                            THROUGH ITS BD BIOSCIENCES DIVISION

By:      /s/ HOWARD C. BIRNDORF          By:     /s/ VINCENT A. FORLENZA
    ---------------------------------        ----------------------------------
         Authorized Signature                     Authorized Signature

                                             VINCENT A. FORLENZA
       HOWARD C. BIRNDORF                    SENIOR VICE PRESIDENT
       CHAIRMAN & CEO                        TECHNOLOGY, STRATEGY & DEVELOPMENT
   ----------------------------------        ----------------------------------
         Name and Title                           Name and Title

<PAGE>

FIRST REVISED APPENDIX A

U. S. PATENTS AND PATENT APPLICATIONS

     1.   U. S. Patent No. 5,270,184, entitled "Nucleic Acid Target Generation"

     2.   U. S. Patent No. 5,422,252, entitled "Simultaneous Amplification of
          Multiple Targets"

     3.   U. S. Patent No. 5,624,825, entitled "Simultaneous Amplification of
          Multiple Targets"

     4.   U. S. Patent No. 5,455,166, entitled "Strand Displacement
          Amplification"

     5.   U. S. Patent No. 5,712,124, entitled "Strand Displacement
          Amplification"

     6.   U. S. Patent No. 5,536,649, entitled "Decontamination of Nucleic Acid
          Amplification Reactions"

     7.   U. S. Patent No. 5,648,211, entitled "Strand Displacement
          Amplification Using Thermophilic Enzymes"

     8.   U. S. Patent No. 5,744,311, entitled "Strand Displacement
          Amplification Using Thermophilic Enzymes"

     9.   U. S. Patent No. 5,702,926, entitled "Use of Boronated Nucleotides in
          Strand Displacement Amplification"

     10.  U. S. Patent No. 5,916,779, entitled "Reverse Transcription Strand
          Displacement Amplification"

     11.  ***

     12.  ***

     13.  ***

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*** Confidential material redacted and separately filed with the Commission.