In this paper, we address the problem of enhancing the performance (including the system capacity and average user bit error probability) of a multi-user multiple-input multiple-output (MIMO) system for communication from one base station to many mobile stations in multipath Rayleigh fading channels. This problem arises in multi-user space division multiplexing (SDM) systems where multiple independent signal streams can be transmitted in the same frequency band and time slot, through the exploitation of multiple antennas at both the base and mobile stations. The objective of this paper is to devise a multi-user linear space-time precoder for simultaneous channel diagonalization of multi-user channels enabling orthogonal space division multiplexing (OSDM). Our approach is based on diagonalizing the multi-user channel matrices and we use a variation of successive Jacobi rotations. The assumption for this scheme is that the BS knows all the channels and the channel dynamics are quasi-stationary over a block of precoded bits as is typical of indoor, low mobility high speed wireless communications.