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The magnitude response of an unconstrained minimax infinite impulse response digital filter usually has a heavy overshoot in the transition band and large group-delay error near the passband edges. This paper imposes a constraint on the frequency responses and makes the magnitude responses in the transition bands approximate some preset monotonically increasing and/or decreasing functions as well as possible. We present a sequential constrained minimax design method that formulates the design problem as a series of constrained minimax problems with given maximum frequency response error in the transition bands. The method can not only minimizes the maximum error of frequency response on the passband and stopband, but also effectively decreases the magnitude overshoot on the transition bands and the group-delay error near the passband edges. Simulation results demonstrate the effectiveness of the proposed method.