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This work presents a novel blind adaptive beamforming algorithm based on maximum signal-to-interference-and-noise ratio (MSINR) criterion for MC-CDMA uplink system with antenna array. The proposed algorithm namely recursive generalized Lagrange multiplier (RGLM) method has lower computational complexity than the well-known GLM method. Our simulation results show that the proposed algorithm has fast convergence and tracking property. Moreover, it can achieve better BER performance compared to the GLM method although in near-far effect environment.