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In this paper, we address the problem of improving the performance of multiuser space-division multiplexing (SDM) systems where multiple independent signal streams can be transmitted in the same frequency and time slot. The problem is important in multiuser multiple-input multiple-output systems where communication from one base station to many mobile stations can occur simultaneously. Our objective is to devise a multiuser linear space-time precoder for simultaneous channel diagonalization of the multiuser channels enabling SDM. Our new approach is based on diagonalizing the multiuser channel matrices and we use a variation of successive Jacobi rotations. In addition to the diagonalization, our approach attempts to optimize the resultant channel gains for performance enhancement. Our method is valid for both frequency-flat and frequency-selective fading channels but we assume that the base station knows all the channels and that they are quasi-stationary.