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A new beamforming method for direct sequence code division multiple access systems is presented. This method is based on Rayleigh quotient of the despread signal's covariance matrix. Two eigenvector analysis algorithms, simple steepest descend algorithm and an algorithm presented by Luo, are used to obtain the new beamforming method. It is shown that both algorithms result in the same updating equation for the weight vector. The proposed method needs only 2N+1 complex multiplications and 2N-1 complex additions for a single run, where N is the number of antennas in the array. Accuracy of the estimated angle-of-arrival (AOA) and the produced beam pattern are evaluated for the proposed method. Moreover, the performance of the new method in reducing the probability of bit error in is investigated in both fading and non-fading channels. Simulation results show that the proposed method has a satisfactory performance with the added advantage of having small computational complexity.