Blind equalization is a technique for adaptive equalization of a communication channel without the aid of the usual training sequence. Although the Constant Modulus Algorithm (CMA) is one of the most popular adaptive blind equalization algorithms, it suffers from slow convergence rate. A novel enhanced blind equalization technique based on a supervised CMA (S-CMA) is proposed in this paper. The technique is employed to initialize the coefficients of a linear transversal equalizer (LTE) filter in order to provide a fast startup for blind training. It also presents a computational study and simulation results of this newly proposed algorithm compared to other CMA techniques such as conventional CMA, Normalized CMA (N-CMA) and Modified CMA (M-CMA). The simulation results have demonstrated that the proposed algorithm has considerably better performance than others.