An efficient procedure for the approximation of two‐dimensional (2‐D) fan filters is presented. The Chebychev (or min‐max) error criterion is used to measure the optimality of the approximation as opposed to previous designs which use the least‐squares norm. Since the direct solution of a 2‐D Chebychev approximation problem is difficult, a change of variables is introduced to convert the 2‐D approximation problem into an equivalent 1‐D low‐pass filter approximation problem. The response is opptimized in the 1‐D domain, and then the change of variables is applied to obtain the 2‐D filter. Thus the techniques of 1‐D Chebychev approximation are applied to yield a 2‐D fan filter.