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In this paper, we consider the blind multiuser detection problem for asynchronous CDMA systems operating in a multipath environment. Using only the spreading code of the desired user, we first mitigate the effect of multiple access interference (MAI) while employing the constrained optimization. The constant modulus algorithm (CMA) is then applied to reliably recover the transmitted information symbol of the desired user rather than one of the interferers. A computationally efficient adaptive algorithms is also developed. Computer simulations confirm the effectiveness of the new blind approach, and the comparisons with the other blind methods show that a significant performance gain is attained.