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Minimax design of nonlinear-phase FIR Alters with prescribed phase error is considered in this paper. By using a sequential constrained least-squares (SCLS) method, the minimax design is converted into a series of constrained least-squares problems, where the upper-bounds imposed on the frequency response (FR) error converge exponentially to the minimal value of the maximum FR error. Design examples demonstrate the effectiveness of the SCLS method. Comparisons of the performances of the filters designed by the SCLS and some other methods are provided.