This paper proposes a new blind algorithm effective for multiuser detection with an adaptive array antenna. The conventional blind algorithm, known as the Constant Modulus Algorithm (CMA), has two major drawbacks: (i) the convergence speed is not sufficiently fast for usual applications in mobile communications, and (ii) the algorithm is very likely to lock on the path with the largest received power, which means the signal with the second largest power can hardly be extracted. This paper introduces the Recursive Least Squares algorithm for CMA (RLS-CMA) in order to speed the convergence up, and additionally introduces the concept of the orthogonal projection into CMA so as to extract signals with weak power. The proposed CMA with Orthogonal Projection (CMA-OP) sequentially calculates the weight vector of each user under a constraint that the weight vector should be orthogonal to the estimated array response vectors of previously extracted users. Computer simulations demonstrate that the proposed scheme can operate properly in the Rayleigh fading channels under the two-user condition.