Massive multiple-input multiple-output (MIMO) technology is one of the key enablers in the fifth generation mobile communications (5G), in order to accommodate growing traffic demands and to utilize higher super high frequency (SHF) and extremely high frequency (EHF) bands. In the paper, we propose a novel transmit precoding named “nonlinear block multi-diagonalization (NL-BMD) precoding” for multiuser MIMO (MU-MIMO) downlink toward 5G. Our NL-BMD precoding strategy is composed of two essential techniques: block multi-diagonalization (BMD) and adjacent inter-user interference pre-cancellation (IUI-PC). First, as an extension of the conventional block diagonalization (BD) method, the linear BMD precoder for the desired user is computed to incorporate a predetermined number of interfering users, in order to ensure extra degrees of freedom at the transmit array even after null steering. Additionally, adjacent IUI-PC, as a nonlinear operation, is introduced to manage the residual interference partially allowed in BMD computation, with effectively-reduced numerical complexity. It is revealed through computer simulations that the proposed NL-BMD precoding yields up to 67% performance improvement in average sum-rate spectral efficiency and enables large-capacity transmission regardless of the user distribution, compared with the conventional BD precoding.