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In this paper, a modified family of blind equalization algorithms is proposed for use in quadrature amplitude modulation (QAM) based digital communication systems. We have called this family: the generalized multimodulus algorithms: MMA(p, q). This family is derived by introducing two degrees of freedom in the conventional MM criterion. We have shown that one of the members of this family, MM(2, 1), (which, to the best of our knowledge, has never been discussed) exhibits the fastest convergence for 16-QAM signal. The dynamic convergence behavior of MM(2, 1) is analyzed and shown to be conforming with simulation results.