<PAGE>   1
                                                              EXHIBIT 3.(i)2


                            CERTIFICATE OF AMENDMENT
                                   OF RESTATED
                          CERTIFICATE OF INCORPORATION
                                       OF
                        BIOSITE DIAGNOSTICS INCORPORATED


                  Biosite Diagnostics Incorporated, a corporation organized and
existing under and by virtue of the General Corporation Law of the State of
Delaware, DOES HEREBY CERTIFY:

                  FIRST: That resolutions were duly adopted by the Board of
Directors of Biosite Diagnostics Incorporated, providing that the Restated
Certificate of Incorporation of the Corporation be amended by changing so much
of Section (A) of Article IV as now reads:

                                   "ARTICLE IV

         (A) Classes of Stock. The total number of shares of all classes of
capital stock which the corporation shall have authority to issue is Twenty
Million Three Hundred Twenty-Eight Thousand Eight Hundred Forty-Seven
(20,328,847) of which Twelve Million (12,000,000) shares of the par value of One
Cent ($.01) each shall be Common Stock (the "Common Stock") and Eight Million
Three Hundred Twenty-Eight Thousand Eight Hundred Forty-Seven (8,328,847)
shares of the par value of One Cent ($.01) each shall be Preferred Stock (the
"Preferred Stock").

         The Preferred Stock shall be designated the "Series A Preferred Stock,"
the "Series B Preferred Stock," the "Series C Preferred Stock," the "Series D
Preferred Stock" and the Series E Preferred Stock, which series shall consist of
610,000 shares, 2,156,336 shares, 2,204,167 shares, 1,900,010 shares and
1,458,334 shares, respectively.

         Subject to Section 6, the Preferred Stock may be issued from time to
time in one or more series. Except for the Series A Preferred Stock, the Series
B Preferred Stock, the Series C Preferred Stock, the Series D Preferred Stock
and the Series E Preferred Stock, the Board of Directors is authorized to fix
the number of shares of any series of Preferred Stock and to determine the
designation of any such shares. The Board of Directors is also authorized to
determine or alter the rights (including, but not limited to, the voting
rights), preferences, privileges and restrictions granted to or imposed upon any
wholly unissued series of Preferred Stock, and within the limits and
restrictions stated in any resolution or resolutions of the Board of Directors
originally fixing the number of shares constituting any series, to increase or
decrease (but not below the number of shares of such series then outstanding)
the number of shares of any such series subsequent to the issue of shares of
that series by filing a certificate pursuant to the applicable law of the State
of Delaware."

to read as follows:
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                                   "ARTICLE IV

         (A) Classes of Stock. The total number of shares of all classes of
capital stock which the corporation shall have authority to issue is Thirty
Million (30,000,000) of which Twenty-One Million Six Hundred Seventy-One
Thousand One Hundred Fifty-Three (21,671,153) shares of the par value of One
Cent ($.01) each shall be Common Stock (the "Common Stock") and Eight Million
Three Hundred Twenty-Eight Thousand Eight Hundred Forty-Seven (8,328,847)
shares of the par value of One Cent ($.01) each shall be Preferred Stock (the
"Preferred Stock").

         The Preferred Stock shall be designated the "Series A Preferred Stock,"
the "Series B Preferred Stock," the "Series C Preferred Stock," the "Series D
Preferred Stock" and the Series E Preferred Stock, which series shall consist of
610,000 shares, 2,156,336 shares, 2,204,167 shares, 1,900,010 shares and
1,458,334 shares, respectively.

         Subject to Section 6, the Preferred Stock may be issued from time to
time in one or more series. Except for the Series A Preferred Stock, the Series
B Preferred Stock, the Series C Preferred Stock, the Series D Preferred Stock
and the Series E Preferred Stock, the Board of Directors is authorized to fix
the number of shares of any series of Preferred Stock and to determine the
designation of any such shares. The Board of Directors is also authorized to
determine or alter the rights (including, but not limited to, the voting
rights), preferences, privileges and restrictions granted to or imposed upon any
wholly unissued series of Preferred Stock, and within the limits and
restrictions stated in any resolution or resolutions of the Board of Directors
originally fixing the number of shares constituting any series, to increase or
decrease (but not below the number of shares of such series then outstanding)
the number of shares of any such series subsequent to the issue of shares of
that series by filing a certificate pursuant to the applicable law of the State
of Delaware."



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                  SECOND: That said amendment was duly adopted in accordance
with the provisions of section 242 of the General Corporation Law of the State
of Delaware. Written consent of the stockholders has been given with respect to
the foregoing amendment in accordance with section 228 of the General
Corporation Law of the State of Delaware, and written notice has been given as
provided in section 228.

   
                  IN WITNESS WHEREOF, said corporation has caused this
certificate to be signed by Kim D. Blickenstaff, its President, and attested by
Christopher J. Twomey, its Assistant Secretary, as of this 5th day of
February, 1997.
    



   
                                               By  /s/ KIM D. BLICKENSTAFF
                                                   --------------------------
                                                       Kim D. Blickenstaff
                                                            President
    


   
Attest:


  /s/ CHRISTOPHER J. TWOMEY
-----------------------------------
   Christopher J. Twomey
   Assistant Secretary
    


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