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Multi-user multiple-input and multiple-output (MU-MIMO) wireless systems have the potential to increase system capacity significantly by separating multiple users in the space domain through appropriate signal processing. These techniques require accurate channel state information at transmitter (CSIT) for their proper operations. With inevitable channel imperfections in practice, robustness has become an important issue in the development of beamforming techniques. In this work, we propose a robust leakage-based transmit beamforming design for multi-user MIMO systems by introducing a probabilistic constraint. In a multi-user system, the main challenge for transmit beamforming is to suppress the co-channel interference (CCI) from other users. Our approach optimizes the average signal-to-interference-plus-noise ratio (SINR) performance implicitly by maximizing the average signal power subject to probabilistic leakage and noise power constraint. Moreover, both the single-stream-per-user and multiple-stream-per-user cases are considered.In the latter case, a hybrid scheme is suggested by incorporating Alamouti code into the proposed design. Simulation results show that under proper control of the probabilistic constraint, both beamformers achieve good bit-error-rate (BER) performances, reliability of SINR levels as well as robustness against channel uncertainties.