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                                                                     Exhibit 3.4

                                                               STATE OF DELAWARE
                                                              SECRETARY OF STATE
                                                        DIVISION OF CORPORATIONS
                                                       FILED 03:00 PM 09/18/2002
                                                             020581984 - 2133133

                          CERTIFICATE OF DESIGNATIONS
                                       of
                 SERIES A JUNIOR PARTICIPATING PREFERRED STOCK
                                       of
                             GEN-PROBE INCORPORATED
                        (Pursuant to Section 151 of the
                       Delaware General Corporation Law)

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

     Gen-Probe Incorporated, a corporation organized and existing under the
General Corporation Law of the State of Delaware (hereinafter called the
"Corporation"), hereby certifies that the following resolution was adopted by
the Board of Directors of the Corporation as required by Section 151 of the
General Corporation Law at a meeting duly called and held on September 16, 2002.

     RESOLVED, that pursuant to the authority granted to and vested in the
Board of Directors of this Corporation (hereinafter called the "Board of
Directors" or the "Board") in accordance with the provisions of the Certificate
of Incorporation of this Corporation, the Board of Directors hereby creates a
series of Preferred Stock, par value $.0001 per share (the "Preferred Stock"),
of the Corporation and hereby states the designation and number of shares, and
fixes the relative rights, powers and preferences, and qualifications,
limitations and restrictions thereof as follows:

     Section 1.     Designation and Amount. The shares of such series shall be
designated as "Series A Junior Participating Preferred Stock" (the "Series A
Preferred Stock") and the number of shares constituting the Series A Preferred
Stock shall be 1,000,000. Such number of shares may be increased or decreased
by resolution of the Board of Directors; provided, that no decrease shall
reduce the number of shares of Series A Preferred Stock to a number less than
the number of shares then outstanding plus the number of shares reserved for
issuance upon the exercise of outstanding options, rights or warrants or upon
the conversion of any outstanding securities issued by the Corporation
convertible into Series A Preferred Stock.

     Section 2.     Dividends and Distributions.

            (A)     Subject to the prior and superior rights of the holders of
     any shares of any class or series of stock of this Corporation ranking
     prior and superior to the Series A Preferred Stock with respect to
     dividends, the holders of shares of Series A Preferred Stock, in preference
     to the holders of Common Stock, par value $.0001 per share (the "Common
     Stock"), of the Corporation, and of any other stock ranking junior to the
     Series A Preferred Stock, shall be entitled to receive, when, as and if
     declared by the Board of Directors out of funds legally available for the
     purpose, quarterly dividends payable in cash on the first day of March,
     June, September and December in each year (each such date being referred to
     herein as a "Quarterly Dividend Payment Date"), commencing on the first
     Quarterly Dividend Payment Date after the first issuance of a share or
     fraction of a share of Series A Preferred Stock, in an amount per share
     (rounded to the nearest cent) equal to the greater of (a) $1.00 or (b)
     subject to the provision for adjustment hereinafter set forth, 100 times
     the aggregate per share amount of all cash dividends, and 100 times
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the aggregate per share amount (payable in kind) of all non-cash dividends or
other distributions, other than a dividend payable in shares of Common Stock or
a subdivision of the outstanding shares of Common Stock (by reclassification or
otherwise), declared on the Common Stock since the immediately preceding
Quarterly Dividend Payment Date or, with respect to the first Quarterly Dividend
Payment Date, since the first issuance of any share or fraction of a share of
Series A Preferred Stock. In the event the Corporation shall at any time declare
or pay any dividend on the Common Stock payable in shares of Common Stock, or
effect a subdivision, combination or consolidation of the outstanding shares of
Common Stock (by reclassification or otherwise than by payment of a dividend in
shares of Common Stock) into a greater or lesser number of shares of Common
Stock, then in each such case the amount to which holders of shares of Series A
Preferred Stock were entitled immediately prior to such event under clause (b)
of the preceding sentence shall be adjusted by multiplying such amount by a
fraction, the numerator of which is the number of shares of Common Stock
outstanding immediately after such event and the denominator of which is the
number of shares of Common Stock that were outstanding immediately prior to such
event.

          (B)  The Corporation shall declare a dividend or distribution on the
Series A Preferred Stock as provided in paragraph (A) of this Section 2
immediately after it declares a dividend or distribution on the Common Stock
(other than a dividend payable in shares of Common Stock); provided that, in the
event no dividend or distribution shall have been declared on the Common Stock
during the period between any Quarterly Dividend Payment Date and the next
subsequent Quarterly Dividend Payment Date, a dividend of $1.00 per share on the
Series A Preferred Stock shall nevertheless be payable on such subsequent
Quarterly Dividend Payment Date.

          (C)  Dividends shall begin to accrue and be cumulative on outstanding
shares of Series A Preferred Stock from the Quarterly Dividend Payment Date next
preceding the date of issue of such shares, unless the date of issue of such
shares is prior to the record date for the first Quarterly Dividend Payment
Date, in which case dividends on such shares shall begin to accrue from the date
of issue of such shares, or unless the date of issue is a Quarterly Dividend
Payment Date or is a date after the record date for the determination of holders
of shares of Series A Preferred Stock entitled to receive a quarterly dividend
and before such Quarterly Dividend Payment Date, in either of which events such
dividends shall begin to accrue and be cumulative from such Quarterly Dividend
Payment Date. Accrued but unpaid dividends shall not bear interest. Dividends
paid on the shares of Series A Preferred Stock in an amount less than the total
amount of such dividends at the time accrued and payable on such shares shall be
allocated pro rata on a share-by-share basis among all such shares at the time
outstanding. The Board of Directors may fix a record date for the determination
of holders of shares of Series A Preferred Stock entitled to receive payment of
a dividend or distribution declared thereon, which record date shall be not more
than 60 days prior to the date fixed for the payment thereof.

     Section 3.     Voting Rights.   The holders of shares of Series A Preferred
Stock shall have the following voting rights:



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               (A)  Subject to the provision for adjustment hereinafter set
forth, each share of Series A Preferred Stock shall entitle the holder thereof
to 100 votes on all matters submitted to a vote of the stockholders of the
Corporation. In the event the Corporation shall at any time declare or pay any
dividend on the Common Stock payable in shares of Common Stock, or effect a
subdivision, combination or consolidation of the outstanding shares of Common
Stock (by reclassification or otherwise than by payment of a dividend in shares
of Common Stock) into a greater or lesser number of shares of Common Stock,
then in each such case the number of votes per share to which holders of shares
of Series A Preferred Stock were entitled immediately prior to such event
shall be adjusted by multiplying such number by a fraction, the numerator of
which is the number of shares of Common Stock outstanding immediately after
such event and the denominator of which is the number of shares of Common Stock
that were outstanding immediately prior to such event.

               (B)  Except as otherwise provided herein, in any other
Certificate of Designations creating a series of Preferred Stock or any similar
stock, or by law, the holders of shares of Series A Preferred Stock and the
holders of shares of Common Stock and any other capital stock of the
Corporation having general voting rights shall vote together as one class on
all matters submitted to a vote of stockholders of the Corporation.

               (C)  Except as set forth herein, or as otherwise provided by
law, holders of Series A Preferred Stock shall have no special voting rights
and their consent shall not be required (except to the extent they are entitled
to vote with holders of Common Stock as set forth herein) for taking any
corporate action.

     Section 4.  Certain Restrictions.
                 ------- ------------

               (A)  Whenever quarterly dividends or other dividends or
distributions payable on the Series A Preferred Stock as provided in Section 2
are in arrears, thereafter and until all accrued and unpaid dividends and
distributions, whether or not declared, on shares of Series A Preferred Stock
outstanding shall have been paid in full, the Corporation shall not:

                    (i)  declare or pay dividends, or make any other
     distributions, on any shares of stock ranking junior (either as to
     dividends or upon liquidation, dissolution or winding up)  to the Series A
     Preferred Stock;

                    (ii)  declare or pay dividends, or make any other
     distributions, on any shares of stock ranking on a parity (either as to
     dividends or upon liquidation, dissolution or winding up) with the Series A
     Preferred Stock, except dividends paid ratably on the Series A Preferred
     Stock and all such parity stock on which dividends are payable or in
     arrears in proportion to the total amounts to which the holders of all such
     shares are then entitled;

                    (iii)  redeem or purchase or otherwise acquire for
     consideration shares of any stock ranking junior (either as to dividends or
     upon liquidation,
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          dissolution or winding up) to the Series A Preferred Stock, provided
          that the Corporation may at any time redeem, purchase or otherwise
          acquire shares of any such junior stock in exchange for shares of any
          stock of the Corporation ranking junior (both as to dividends and upon
          dissolution, liquidation or winding up) to the Series A Preferred
          Stock; or

                    (iv)  redeem or purchase or otherwise acquire for
          consideration any shares of Series A Preferred Stock, or any shares of
          stock ranking on a parity with the Series A Preferred Stock, except in
          accordance with a purchase offer made in writing or by publication (as
          determined by the Board of Directors) to all holders of such shares
          upon such terms as the Board of Directors, after consideration of the
          respective annual dividend rates and other relative rights and
          preferences of the respective series and classes, shall determine in
          good faith will result in fair and equitable treatment among the
          respective series or classes.

               (B)  The Corporation shall not permit any subsidiary of the
     Corporation to purchase or otherwise acquire for consideration any shares
     of stock of the Corporation unless the Corporation could, under paragraph
     (A) of this Section 4, purchase or otherwise acquire such shares at such
     time and in such manner.

          Section 5.  Reacquired Shares. Any shares of Series A Preferred Stock
purchased or otherwise acquired by the Corporation in any manner whatsoever
shall be retired and canceled promptly after the acquisition thereof. All such
shares shall upon their cancellation become authorized but unissued shares of
Preferred Stock and may be reissued as part of a new series of Preferred Stock
subject to the conditions and restrictions on issuance set forth herein, in the
Certificate of Incorporation, or in any other Certificate of Designations
creating a series of Preferred Stock or any similar stock or as otherwise
required by law.

          Section 6.  Liquidation, Dissolution or Winding Up.

               (A)  Upon any liquidation, dissolution or winding up of the
     Corporation, voluntary or otherwise, no distribution shall be made (1) to
     the holders of shares of stock ranking junior (either as to dividends or
     upon liquidation, dissolution or winding up) to the Series A Preferred
     Stock unless, prior thereto, the holders of shares of Series A Preferred
     Stock shall have received an amount per share (the "Series A Liquidation
     Preference") equal to $100 per share, plus an amount equal to accrued and
     unpaid dividends and distributions thereon, whether or not declared, to the
     date of such payment, provided that the holders of shares of Series A
     Preferred Stock shall be entitled to receive an aggregate amount per share,
     subject to the provision for adjustment hereinafter set forth, equal to 100
     times the aggregate amount to be distributed per share to holders of shares
     of Common Stock, or (2) to the holders of shares of stock ranking on a
     parity (either as to dividends or upon liquidation, dissolution or winding
     up) with the Series A Preferred Stock, except distributions made ratably on
     the Series A Preferred Stock and all such parity stock in proportion to the
     total amounts to which the holders of all such shares are entitled upon
     such liquidation, dissolution or winding up. In the event the Corporation
     shall at any time declare of pay any dividend on the Common Stock payable
     in shares of Common Stock, or effect a subdivision, combination or


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that any such other series specifically provides that it shall rank on a parity
with or junior to the Series A Preferred Stock.

          Section 10. Amendment. At any time any shares of Series A Preferred
Stock are outstanding, the Certificate of Incorporation of the Corporation
shall not be amended in any manner which would materially alter or change the
powers, preferences or special rights of the Series A Preferred Stock so as to
affect them adversely without the affirmative vote of the holders of at least
two-thirds of the outstanding shares of Series A Preferred Stock, voting
separately as a single class.

          Section 11. Fractional Shares. Series A Preferred Stock may be issued
in fractions of a share that shall entitle the holder, in proportion to such
holder's fractional shares, to exercise voting rights, receive dividends,
participate in distributions and to have the benefit of all other rights of
holders of Series A Preferred Stock.

               IN WITNESS WHEREOF, this Certificate of Designations is executed
on behalf of the Corporation by its Vice President, General Counsel and
Assistant Secretary this 17th day of September, 2002.


                                             /s/ R. William Bowen
                                             -----------------------------------
                                             R. William Bowen
                                             Vice President, General Counsel
                                             and Assistant Secretary