We design a precoder for non-concurrent two-way relaying (ncTWR) where a base station (BS) serves a transmit-only user equipment (TUE) in the uplink and a receive-only user equipment (RUE) in the downlink. The RUE experiences back-propagating interference (BI). The proposed precoder is designed such that it not only cancels the BI experienced by the RUE but more importantly, enables receive data decoding with high diversity. The high diversity precoder is designed by deriving the closed-form pairwise error probability (PEP) expressions, and by optimizing the precoder elements to minimize the PEP. We analytically show that with Nr -antenna relay, Nb-antenna BS, and Nu-antenna TUE and RUE, both BS and RUE decode their respective data with a diversity order of -(Nu 2,(Nr-Nu)Nb) at high receive signal-to-noise ratio. We also numerically show that the proposed design has lower bit error rate than the existing state-of-the-art ncTWR designs. © 1972-2012 IEEE.