We investigate a joint design of linear precoders and receivers for multiple-input multiple-output non-simultaneous two-way relaying (NS-TWR). Unlike conventional two-way relaying, the base station in NS-TWR performs two-way relaying with two different users - a transmit-only user and a receive-only user (RUE). The RUE experiences back-propagating interference (BI). The proposed design cancels this BI and provides beamforming gain over existing designs. For NS-TWR, we maximize the weighted sum-rate (WSR) through joint power allocation, by solving a sequence of geometric programs. The precoder and the receiver designs as well as the power allocation program are then extended for a multi-user system with multiple transmit-only and receive-only users. With exhaustive simulations, we show that the proposed design provides significantly better WSR than the existing ones. The proposed design is also evaluated in a cellular framework using realistic path loss models, to assess the system-level performance gain achievable. © 2002-2012 IEEE.