
<PAGE>   1
                                                                    EXHIBIT 20.1



AT THE COMPANY:                     AT THE FINANCIAL RELATIONS BOARD:
F. Robert Merrill                   Karl Plath                 Kate Rajeck
Sr. Vice-President/Finance          General Inquiries          Analyst Inquiries
214-390-9800                        312-640-6738               312-640-6669


                QUEST MEDICAL, INC. REDEEMS OUTSTANDING RIGHTS;
                      ADOPTS NEW SHAREHOLDERS' RIGHTS PLAN

DALLAS, AUGUST 30, 1996-QUEST MEDICAL, INC. (NASDAQ: QMED) announced today that
its Board of Directors has voted to redeem the outstanding rights issued under
the Shareholders' Rights Plan adopted in 1989, at the pre-established
redemption price of 1 cent per right, and has adopted a new Shareholders'
Rights Plan in which Rights to purchase shares of Quest Medical's Common Stock
will be distributed as a dividend, one Right per share, to record owners of
Quest Medical's Common Stock as of the close of business on September 12, 1996.
The Shareholders' Rights Plan was not adopted in response to any known offers
for Quest Medical, Inc.

     Quest Medical's Board of Directors noted in a letter to shareholders that
the action was being taken to replace the old plan, which was already scheduled
to expire in 1999 and to implement a number of innovators that have developed
over the last several years to ensure that the plan would have its intended
effect of enhancing shareholder value.  The new Plan is designed to require
that any potential acquirer seeking to obtain control of Quest Medical treat
all Quest Medical shareholders fairly and equally and to deter the use of
coercive takeover tactics.

     "The Board has been considering adopting a new plan for several weeks,"
said Chairman Richard A. Gilleland.  Just recently, a Quest Medical shareholder
urged the Board to put the company up for sale or seek a merger partner.  The
Board has since stated publicly that the company is not for sale.

     "In the event of an unsolicited offer," Gilleland added, "the Board
believes that the new Plan will enable it to take the necessary time to
evaluate the proposal and to make sure that shareholder value is enhanced.  The
Board is not aware of any actual effort to acquire control of Quest Medical and
the new Plan is not being adopted in response to the shareholder's
recommendation or any other specific event.  We believe that the current market
and economic environment make the redemption of the existing rights and the
adoption of the new Plan prudent steps to take at this time."

     Upon becoming exercisable, each Right entitles holders to purchase one
share of Common Stock for $30.00.  The rights are not exercisable, however,
until a person or group acquires more than 15 percent of Quest Medical's common
stock or announces a tender or exchange offer for more than 20 percent of the
stock.  The purchase price and number of shares purchasable will be adjusted if
a person or group acquires more than 15 percent of Quest Medical's common
stock.

     Details of the Plan and the Rights are outlined in a letter that is being
mailed to all Quest Medical shareholders.



<PAGE>   2


QUEST MEDICAL, INC.




     Dallas-based Quest Medical designs, develops, manufactures and markets a
variety of healthcare products used primarily in cardiovascular surgery,
interventional pain management and intravenous fluid delivery applications.


