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Block diagonalization (BD) is a well-known precoding method in multiuser multi-input multi-output (MIMO) broadcast channels. This scheme can be considered as a extension of the zero-forcing (ZF) channel inversion to the case where each receiver is equipped with multiple antennas. One of the limitation of the BD is that the sum rate does not grow linearly with the number of users and transmit antennas at low and medium signal-to-noise ratio regime, since the complete suppression of multi-user interference is achieved at the expense of noise enhancement. Also it performs poorly under imperfect channel state information. In this paper, we propose a generalized minimum mean-squared error (MMSE) channel inversion algorithm for users with multiple antennas to overcome the drawbacks of the BD for multiuser MIMO systems. We first introduce a generalized ZF channel inversion algorithm as a new approach of the conventional BD. Applying this idea to the MMSE channel inversion for identifying orthonormal basis vectors of the precoder, and employing the MMSE criterion for finding its combining matrix, the proposed scheme increases the signal-to-interference-plus-noise ratio at each user's receiver. Simulation results confirm that the proposed scheme exhibits a linear growth of the sum rate, as opposed to the BD scheme. For block fading channels with four transmit antennas, the proposed scheme provides a 3 dB gain over the conventional BD scheme at 1% frame error rate. Also, we present a modified precoding method for systems with channel estimation errors and show that the proposed algorithm is robust to channel estimation errors.