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A modification to the well-known constant modulus algorithm (CMA) for blind channel equalization is proposed. The conventional CMA has rotational ambiguity and hence cannot achieve carrier phase recovery. It happens because the cost function is made up of the absolute value of the equalizer output and phase information is not used. In this paper, we slightly modify the cost function and provide a different error function that restores the phase of the carrier. Simulations studies are shown for the case of 16-QAM signal constellation.