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A minimax infinite impulse response (IIR) digital filter often has an obvious magnitude overshoot in the transition band and a large group delay error near the passband edge. We recently presented a sequential constrained minimax (SCMM) method to design IIR filters with reduced magnitude overshoot and group delay error. In this paper, we combine the SCMM method with a sequential minimization procedure based on second-order factor updates (SMSOF) to further improve the design results by using stability triangles as the stability constraints. Design examples demonstrate that the proposed method not only makes the maximum frequency response error on the passband and stopband as small as possible, but also reduces the magnitude overshoot in the transition band and the group delay error near the passband edge.