Tomlinson-Harashima precoding (THP) is a nonlinear processing technique employed at the transmit side which is a dual to the successive interference cancelation (SIC) detection at the receive side. Like SIC detection, the performance of THP strongly depends on the ordering of the precoded symbols. The optimal ordering algorithm, however, is impractical for multiuser MIMO (MU-MIMO) systems with multiple receive antennas due to the fact that the users are geographically distributed. In this paper, we propose a multi-branch THP (MB-THP) scheme and algorithms that employ multiple transmit processing and ordering strategies along with a selection scheme to mitigate interference in MU-MIMO systems. Two types of multi-branch THP (MB-THP) structures are proposed. The first one employs a decentralized strategy with diagonal weighted filters at the receivers of the users and the second uses a diagonal weighted filter at the transmitter. The MB-MMSE-THP algorithms are also derived based on an extended system model with the aid of an LQ decomposition, which is much simpler compared to the conventional MMSE-THP algorithms. Simulation results show that a better bit error rate (BER) performance can be achieved by the proposed MB-MMSE-THP precoder with a small computational complexity increase.