<PAGE>   1


                                                                   EXHIBIT 10.34

                   FIRST AMENDMENT TO STOCK PURCHASE AGREEMENT


         THIS FIRST AMENDMENT TO STOCK PURCHASE AGREEMENT (this "Amendment") is
dated as of the 14th day of December 1999, by and among Horizon Medical
Products, Inc., a Georgia corporation, ("Purchaser"), Stepic Corporation, a New
York corporation ("Stepic"), and Steven Picheny, Howard Fuchs and Christine
Selby (collectively, the "Stepic Shareholders").

                                   WITNESSETH:


         WHEREAS, Purchaser, Stepic and the Stepic Shareholders are parties to
that certain Stock Purchase Agreement, dated as of, and effective as of October
15, 1998 (the "Stock Purchase Agreement"); and

         WHEREAS, Purchaser, Stepic and the Stepic Shareholders desire to amend
certain provisions of the Stock Purchase Agreement;

         NOW, THEREFORE, in consideration of the premises and the mutual
promises and agreements contained herein and other good and valuable
consideration, the receipt and sufficiency of which are hereby acknowledged, the
parties hereto, intending to be legally bound, hereby agree as follows:

         1.       Section 1.2(b) of the Stock Purchase Agreement is hereby
deleted and replaced in its entirety with the following:

                  "(b) $4,000,000, plus $450,834 as an acceleration of the
         payment due pursuant to Section 1.3(d) hereof (the "First Anniversary
         Payment"), payable within 60 days after the first anniversary of the
         Closing Date (as defined in Section 6.1 hereof) (the "First Anniversary
         Date"), and payable as follows:

                           (i)      $2,400,000 payable on December 15, 1999
                  under the Standby Letters of Credit issued to the Stepic
                  Shareholders and apportioned among Stepic Shareholders as
                  follows:

<TABLE>
                                    <S>                        <C>
                                    Steven Picheny             $2,112,000;
                                    Howard Fuchs               $  144,000;
                                    Christine Selby            $  144,000.
</TABLE>

                  Each Standby Letter of Credit shall be reduced by an amount
                  equal to the payment made pursuant to this Section 1.2(b)(i)
                  under such Standby Letter of Credit;
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                           (ii)     $1,400,000 payable in cash on December 15,
                  1999 and apportioned among Stepic Shareholders as follows:

<TABLE>
                                    <S>                        <C>
                                    Steven Picheny             $980,000;
                                    Howard Fuchs               $210,000;
                                    Christine Selby            $210,000; and
</TABLE>

                           (iii)    $650,834, plus $54,873.30 in interest due on
                  the First Anniversary Payment pursuant to Section 1.6, for a
                  total of $705,707.30, plus simple interest on the unpaid
                  balance of this amount which shall accrue at a rate equal to
                  11% per annum, based on a 365-day year and on actual days
                  elapsed, payable in installments as follows:

                                    (A)      $225,000 payable in installments of
                           $25,000 on each of December 15, 1999, December 22,
                           1999, December 29, 1999, January 5, 2000, January 12,
                           2000, January 19, 2000, January 26, 2000, February 2,
                           2000 and February 9, 2000, with each installment
                           apportioned among Stepic Shareholders as follows:

<TABLE>
                                             <S>                                          <C>
                                             Steven Picheny                               70%;
                                             Howard Fuchs                                 15%;
                                             Christine Selby                              15%; and
</TABLE>

                                    (B)      The remainder payable in weekly
                           installments of $50,000 each Wednesday beginning on
                           February 16, 2000 until all principal amounts plus
                           accrued interest have been paid, with each
                           installment apportioned among Stepic Shareholders as
                           follows:

<TABLE>
                                            <S>                                          <C>
                                            Steven Picheny                               70%;
                                            Howard Fuchs                                 15%;
                                            Christine Selby                              15%.
</TABLE>

                  Payments made under this Section 1.2(b)(iii) shall be applied
                  first to accrued interest and then to the remaining principal
                  balance."


         2.       Section 1.3(f) of the Stock Purchase Agreement is hereby
deleted and replaced in its entirety with the following:

                           "(f)     Notwithstanding anything herein to the
                  contrary, any amounts payable on the Second or Third
                  Anniversary Date that are not being disputed pursuant to
                  Section 1.3(e) or subject to Offset (as hereinafter defined)
                  shall be paid within 60 days of the Second or Third
                  Anniversary Date, respectively."
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         3.       Section 1.6 of the Stock Purchase Agreement is hereby deleted
and replaced in its entirety with the following:

                  "Section 1.6 Interest. With respect to the Second Anniversary
         Payment and the Third Anniversary Payment, Purchaser will pay interest
         on the amount of each unpaid portion of each payment for the period
         beginning on the day after the Second Anniversary Date and the Third
         Anniversary Date, as applicable, and continuing through the date of
         payment. Interest will be calculated as simple interest on a per annum
         basis equal to the prime rate (Chase Manhattan Bank) less 1%. Any
         interest payable hereunder shall be paid on the date of payment of the
         applicable installment of the Purchase Price."


         4.       Section 1.8 of the Stock Purchase Agreement is hereby deleted
and replaced in its entirety with the following:

                  "Section 1.8 Apportionment of Purchase Price. The Purchase
         Price shall be apportioned among Stepic Shareholders in proportion to
         each Stepic Shareholder's ownership of Stepic Stock as reflected on
         Schedule 2.2(a) of the Stepic Disclosure Letter (as hereinafter
         defined), except for the First Anniversary Payment, which shall be
         apportioned among Stepic Shareholders as set forth in Section 1.2(b)."


         5.       Article 1 of the Stock Purchase Agreement is hereby amended by
adding the following Section 1.9 thereto:

                  "Section 1.9 Tax Accrual Reimbursement. On December 15, 1999,
         Purchaser shall pay Stepic Shareholders an amount equal to $27,266 as
         reimbursement for the over-accrual of taxes due to New York City and to
         the State of New York, as reflected on the Closing Balance Sheet, in
         full settlement of such over-accrual amount. The parties agree that
         such $27,266 payment shall be treated as an excess payment pursuant to
         Section 1.3(d)(i) which will result first in a reduction in the amount
         of the Third Anniversary Payment and thereafter a reduction in the
         Second Anniversary Payment. The parties further agree that such payment
         shall be apportioned among the Stepic Shareholders as follows: Steven
         Picheny (100%); Howard Fuchs (0%); and Christine Selby (0%)."


         6.       This Amendment may be executed in counterparts, all of which
together shall constitute one in the same instrument.


         7.       Except as expressly amended hereby, the Stock Purchase
Agreement shall continue in full force and effect. This Amendment is limited as
written and should not be deemed to be a consent or waiver of any other term or
condition of the Stock Purchase Agreement.

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         IN WITNESS WHEREOF, the parties have executed this First Amendment to
Stock Purchase Agreement to be duly executed, as of the date first above
written.


                                       HORIZON MEDICAL PRODUCTS, INC.


                                       By:      /s/ WILLIAM E. PETERSON, JR.
                                          --------------------------------------
                                          William E. Peterson, Jr.
                                          President


                                       STEPIC CORPORATION


                                       By:      /s/ STEVEN PICHENY
                                          --------------------------------------
                                          Steven Picheny
                                          President


                                       STEPIC SHAREHOLDERS


                                       By:      /s/ STEVEN PICHENY
                                          --------------------------------------
                                          Steven Picheny


                                       By:      /s/ HOWARD FUCHS
                                          --------------------------------------
                                          Howard Fuchs


                                       By:      /s/ CHRISTINE SELBY
                                          --------------------------------------
                                          Christine Selby