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This paper presents an idea for enhancing the convergence rate of the blind constant modulus algorithm which is used in spatial filtering (beam forming) of the users in a typical CDMA environment. The convergence rate is increased by initializing the weights of the CMA using a non-blind algorithm least mean squares (LMS) utilizing only a few samples of training sequence. Performance as well as convergence of the algorithm have been enhanced using this technique. Computer simulations are presented to show the improved performance of this technique.