Summary: We propose the improvement of the successive projections (SP) method so that the obtained solution becomes an optimum in the Chebyshev sense. In the previous SP method, we obtained the solution satisfying the prescribed allowable deviation from the desired frequency response. However, this solution is not necessarily an optimum in the Chebyshev sense. Then, in the proposed method, the average of local maximum error in the \(n\)th iteration is selected as the maximum allowable deviation in the next iteration. The algorithm is iterated until the absolute maximum error between the desired frequency response and designed response becomes equiripple.