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In this paper we consider multi-user detection in CDMA systems. A modified recursive least squares (RLS) blind adaptive algorithm for multiuser detection in multipath channels is proposed. The proposed algorithm is shown to have a lower computational complexity than the conventional RLS algorithm while maintaining the same performance as the conventional RLS algorithm. Also, we propose a blind adaptive RLS algorithm that is used for multiuser detection of the high rate users in dual rate DS/CDMA systems in multipath (MP) fading channels. The new algorithm gives the same performance as the previously studied cyclic RLS algorithms. However, it has a significantly lower computational complexity.