Blind equalization is a technique of adapting an equalizer without the need of a training sequence. The constant modulus algorithm (CMA) is one of the first known blind equalization algorithms. The cost function of the CMA exhibits local minima, which are the primary cause of the ill-convergence of the CMA. Using the CMA with an anchored equalizer greatly improves the performance of the CMA in terms of ill-convergence. This technique is used in this paper with the linear and the decision feedback equalizers. Theory and simulation show that such an adaptive equalizer will always remove intersymbol interference (ISI) provided the main cursor's gain exceeds a certain critical value.