This study investigated the crucial-but not well-discussed-issues involved in designing beamforming for all receivers, subject to leakage power constraints. Our assumption is that all users use ordered successive interference cancellation (OSIC) detection when the channel state information (CSI) is available. The problem of interest is to find beamforming that can improve OSIC performance of a multi-user scheme without significantly increasing the complexity. This study considers the transceiver design for multi-user MIMO (MU-MIMO) communications, in which a single transmitter adopts beamforming to simultaneously transmit information at first time-slot. During the second time-slot, receivers cooperate to share specific results of OSIC detection in each user. We propose the maximum-likelihood (ML) to estimate the received symbols. The estimated symbols will be used in OSIC detection to detect interference symbols. Promising results show that our cooperative OSIC scheme of the MU-MIMO beamforming system based on maximum signal-to-leakage ratio (SLR) realizes the diversity order of OSIC. Also, by utilizing leakage power as a useful power and not just as an interference power, the performance of the proposed scheme over Rayleigh and Rician channels is significantly better than the performance of classical MU-MIMO beamforming system based on SLR at a high signalto-noise ratio (SNR).