<PAGE>   1


                                                                   Exhibit 3.1.2


                               STATE OF DELAWARE
                        OFFICE OF THE SECRETARY OF STATE


     I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY
CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF AMENDMENT
OF "NORTHSTAR HEALTH SERVICES, INC." FILED IN THIS OFFICE ON THE SIXTEENTH DAY
OF JUNE, A.D. 1998, AT 2 O'CLOCK P.M.

     A FILED COPY OF THIS CERTIFICATE HAS BEEN FORWARDED TO THE NEW CASTLE
COUNTY RECORDER OF DEEDS.






                                             /s/ EDWARD J. FREEL 
                                             -----------------------------------
                                             Edward J. Freel, Secretary of State


2316184 8100                                 AUTHENTICATION:  9141677
981232574                                    DATE:            06-16-98
<PAGE>   2


                                                       STATE OF DELAWARE
                                                       SECRETARY OF STATE
                                                       DIVISION OF CORPORATIONS
                                                       FILED 02:00 PM 06/16/1998
                                                       981232574-2316184


                            CERTIFICATE OF AMENDMENT
                                       OF
                          CERTIFICATE OF INCORPORATION
                                       OF
                        NORTHSTAR HEALTH SERVICES, INC.


     Northstar Health Services, Inc., a corporation organized and existing
under and by virtue of the General Corporation Law of the State of Delaware.

DOES HEREBY CERTIFY THAT:

     FIRST: The Board of Directors of Northstar Health Services, Inc. (the
"Corporation"), at a meeting of the Board of Directors held on April 14, 1998,
pursuant to notice duly given, duly adopted the following resolutions setting
forth a proposed amendment of the previously amended Certificate of
Incorporation of the Corporation, declaring such amendment to be advisable and
calling for a meeting of the stockholders of said Corporation for consideration
thereof. The resolution setting forth the proposed amendment is as follows:

          RESOLVED, that in accordance with Title 8, Chapter 1, Section 242 of
the Delaware Code, as amended, the Board of Directors hereby declares the
advisability of, and hereby approves and adopts, the following proposed
amendment to the Company's Certificate of Incorporation and hereby directs that
the following proposed amendment to the Certificate of Incorporation of this
Company be submitted to the stockholders of the Company for their approval and
adoption at the 1998 Annual Meeting of the Stockholders, to wit:

               Article 4 of the Certificate of Incorporation of Northstar Health
          Services, Inc. is amended and restated to read in full and in its
          entirety as follows:

               4. The total number of shares of stock which the Corporation
          shall have authority to issue is twenty-one million (21,000,000)
          shares, twenty million (20,000,000) shares of which shall be Common
          Stock, of the par value of One Cent ($0.01) per share (the "Common
          Stock"), and one million (1,000,000) shares of which shall be
          Preferred Stock, of the par value of One Cent ($0.01) per share (the
          "Preferred Stock"), amounting in the aggregate to Two Hundred Ten
          Thousand Dollars ($210,000).

               Additional designations and powers, preferences and rights and
          qualifications, limitations or restrictions thereof of the shares of
          stock shall be determined by the Board of Directors of the Corporation
          from time to time. 

     SECOND: Thereafter, pursuant to resolution of the Board of Directors, at
the annual meeting of the stockholders of the Corporation held on June 11,
1998, after notice in accordance with Section 222 of the General Corporation
Law of the State of Delaware, the holders of a majority of the outstanding
shares entitled to vote thereon voted in favor of the approval and adoption of
the amendment.

     THIRD: Such amendment was duly adopted in accordance with the provisions
of Section 242 of the General Corporation Law of the State of Delaware.

     IN WITNESS WHEREOF, said Corporation has caused this Certificate of
Amendment to be signed by Thomas W. Zaucha, its President and Chief Executive
Officer this 11th day of June, 1998.


                         
(SEAL)                                    NORTHSTAR HEALTH SERVICES, INC.


                                          BY: /S/ THOMAS W. ZAUCHA
                                          -------------------------------
                                                  Thomas W. Zaucha
                                          President and Chief Executive Officer