The constant modulus algorithm (CMA) has proved its ability to compensate the severe effect of the multi-path interference and co-channel signals on the constant modulus signals. The application limitation of the CMA is mainly due to its slow rate of convergence. This paper presents a new algorithm, which keeps the desired properties of the original CMA while it reduces the time required for convergence at the expense of some mathematical complexity. The proposed algorithm is derived by analogy to the recursive least squares (RLS) as a fast implementation for the least mean square (LMS) one. The algorithm shows stable operations in both cases of compensating the effect of the multi-path interference by an adaptive correction filter and separation of co-channel signals by an adaptive array followed by a signal canceller. The convergence of the proposed algorithm is an order of magnitude faster than the original CMA on the average.