Tomlinson-Harashima precoding (THP) for downlink MU-MIMO channel can be modeled as user signal perturbation (constellation expansion) followed by linear precoding. The effective linear precoder in standard THP is merely a function of the MU-MIMO channel, which does not provide the flexibility for user power allocation. A modified THP algorithm is proposed so that the effective linear precoder can be arbitrary. As a special case, zero-forcing THP (ZF-THP) with arbitrary user power allocation is considered for which optimal user power allocation is derived to maximize the weighted sum-rate of users.