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We present a multi-user multiple-input multiple-output (MU-MIMO) preceding scheme utilizing generalized singular value decomposition (GSVD). Our work is motivated by the precoding scheme developed by Sadek, Tarighat, and Sayed that maximizes the signal to leakage and noise ratio (SLNR), in which the precoding weight is obtained by the generalized eigenvalue decomposition (GEVD). However, the covariance matrix utilized in GEVD becomes close to be singular as the signal to noise ratio goes high. To improve the numerical accuracy, a GSVD based algorithm is exploited in this paper and a novel method is derived to compute the precoding weights for multiple users by removing redundant computational loads rather than repeating the GSVD algorithm for each user. In addition, we propose a technique to speed up the GSVD based precoding algorithm by preprocessing using the QR decomposition. Finally, to improve the system performance, the antenna selection scheme using GSVD is also proposed which does not require the exhaustive search to choose the active antennas.