In this paper, we propose a method for representing and transforming a systolic design. For representing a systolic design, the generating function [3, 11, 13] is used. The generating function can be used to describe the location, velocity, and moving path of a data item at any given time. Several generating functions can be grouped together to form a "systolic flow". When we use the systolic flow to represent a systolic design and apply a transformation matrix T on it, different generating functions which represent different but equivalent systolic designs of a given computation can be derived. We observe that the different elements in T play different transformation roles; hence, this gives us a guideline to select the elements in the transformation matrix.