We propose a multiuser MIMO precoding algorithm that combines the block Tomlinson-Harashima precoding and the vector perturbation (BTHP-VP). BTHP-VP supports multi-stream transmission without additional estimation of each user's effective channel and achieves full spatial diversity. Computer simulations show that BTHP-VP can achieve similar sum rate and improved BER performance compared to the BTHP with maximum likelihood receiver.