Channel inversion is one of the simplest techniques for multiuser downlink systems with single-antenna users. In this paper, we extend the regularized channel inversion technique developed for the single-antenna user case to multiuser multiple-input multiple-output (MIMO) channels with multiple-antenna users. We first employ the multiuser preprocessing to project the multiuser signals near the null space of the unintended users based on the MMSE criterion, and then the single-user preprocessing is applied to the decomposed MIMO interference channels. In order to reduce the complexity, we focus on non-iterative solutions for the multiuser transmit beamforming and use a linear receiver based on an MMSE criterion. Simulation results show that the proposed scheme outperforms existing joint iterative algorithms in most multiuser configurations.