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Previous precoding algorithms have concentrated on the single user scenario where the precoding scheme assumes perfect channel state information (CSI) at the transmitter or on limited feedback techniques, such as channel quantization or limited feedback signal designs. This paper proposes a novel unitary downlink precoding design scheme for multiuser spatial multiplexing multiple-input multiple-output (MIMO) systems. With the perfect CSI available at the transmitter and the linear decoder at the receiver, the cost function was constructed based on the minimum average probability of vector symbol error and the design method of the precoding matrices was given. These proposed precoding matrices can completely eliminate co-channel interference for each user at the transmitter, and each user will eventually observe an interference-free single user channel, thus simplify the decoding of each user. The impact of channel feedback errors on the system performance and the upper bounds of several schemes for performance comparison were investigated. The simulation results show that the proposed precoding for multiuser spatial multiplexing system obtains almost the same performance as the single user precoding system.