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The minimax design of infinite impulse response (IIR) digital filters is a nonconvex optimization problem, and thus has many local minima. It is shown in this correspondence that a sequential constrained least-squares (SCLS) method has a higher possibility of obtaining better solutions than a direct minimization method when applied to the nonconvex minimax design of IIR filters. We combine the SCLS method with a Steiglitz-McBride (SM) strategy, resulting in a practical design procedure. The positive realness stability condition proposed by Dumitrescu and Niemisto is reformulated as linear inequality constraints and then incorporated in the design procedure. Simulation examples and comparisons with several existing methods demonstrate the effectiveness of the procedure and good performances of the designed filters.