We consider an amplify-and-forward infrastructure non-concurrent two-way relaying (ncTWR) scenario where a base station serves a transmit-only user TUE and a receive-only user RUE. Unlike conventional two-way relaying, the RUE in ncTWR experiences back-propagating interference (BI). Uniform channel decomposition and Tomlinson-Harashima precoding improve the bit error rate (BER) of multiple-antenna-multiple-output (MIMO) systems. Inspired by these techniques, we design a transceiver to reduce BER of both users in MIMO ncTWR. This transceiver cancels BI of the RUE and uses spatial noise whitening filters, designed herein, to uniformly decompose MIMO channels of both TUE and RUE. This letter quantifies the improved BER of the proposed transceiver. © 2012 IEEE.