<PAGE>
CERTAIN MATERIAL (INDICATED BY AN ASTERISK) HAS BEEN OMITTED FROM THIS DOCUMENT
PURSUANT TO A REQUEST FOR CONFIDENTIAL TREATMENTS. THE OMITTED MATERIAL HAS
BEEN FILED SEPARATELY WITH THE SECURITIES AND EXCHANGE COMMISSION.

                                                                   Exhibit 10.20


                                AMENDMENT NO. 1
                                     to the
                               License Agreement
                            Effective April 23, 1997
                                    Between
                              STANFORD UNIVERSITY
                                      and
                             GEN-PROBE INCORPORATED

          Effective April __, 1998 THE BOARD OF TRUSTEES OF THE LELAND STANFORD
JUNIOR UNIVERSITY, having a principal place of business at 900 Welch Road,
Suite 350, Palo Alto, CA 94304 (hereinafter "STANFORD") and GEN-PROBE
INCORPORATED, having a principal place of business at 10210 Genetic Center
Drive, San Diego, CA 92121 (hereinafter "GEN-PROBE"), agree as follows:

                                 1. BACKGROUND

1.1  STANFORD and GEN-PROBE are parties to a License Agreement effective April
     23, 1997 ("Original Agreement") concerning the invention entitled
     "Selective Amplification of Target Polynucleotide Sequences" ("Invention")
     as described in Stanford Docket S87-012.

1.2  STANFORD and GEN-PROBE wish to amend the Original Agreement so that
     GEN-PROBE may practice the Invention in a broadened [***] field of use.

                                 2. AMENDMENTS

2.1  Paragraph 1.8 of the Original Agreement is amended by replacing the words
     "in the Licensed Field of Use, Licensed Product(s), and Licensed Field of
     Use being terms" with the following:

          "in the Licensed Field of Use and the Nonexclusive Field of Use,
          Licensed Product(s), Licensed Field of Use, and Nonexclusive Field of
          Use being terms".

2.2  Paragraph 2.2 of the Original Agreement is amended by inserting in the
     second line the phrase "and the Nonexclusive Field of Use" immediately
     after the phase "Licensed Field of Use".

2.3  Add a new Paragraph "2.9" to the Original Agreement as follows:

          "2.9  "Nonexclusive Field of Use" means [***}.

2.4  Add a new Paragraph "4.4" to the Original Agreement as follows:

          "4.4  STANFORD hereby grants and GEN-PROBE hereby accepts a
                nonexclusive license in the Nonexclusive Field of Use to make,
                have made, use, and sell Licensed Product(s) in the Licensed
                Territory for the life of the last to expire of Licensed
                Patent(s)."


*** Certain information on this page has been omitted and filed separately with
the Commission. Confidential treatment has been requested with respect to the
omitted portions.
<PAGE>
     2.5  All other provisions of the Original Agreement remain in full force
          and effect.

          IN WITNESS WHEREOF, the parties hereto have executed this Amendment
          No. 1 in duplicate originals.

               THE BOARD OF TRUSTEES OF THE LELAND
               STANFORD JUNIOR UNIVERSITY

               By /s/ Katharine Ku
                 --------------------------------------------
                   Director, Office of Technology Licensing

               Date   May 4, 1998
                   -------------------------


               GEN-PROBE INCORPORATED

               By /s/ Henry L. Nordhoff
                 ------------------------------------------
                    Henry L. Nordhoff

               Title President and Chief Executive Officer
                    ---------------------------------------

               Date   April 24, 1998
                   --------------------------

LEGAL DEPT. APPROVAL SEAL


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