Two-way relaying systems efficiently accomplish transmissions in both directions within dual-hop, hence, two time slots can be saved compared with one-way relaying. However, the conventional two-way relaying protocol requires the assumption of symmetric traffic demands, that is, each transmitter node has to act as a receiver in latter slot. This assumption restricts applying two-way relay to general and practical scenarios. In this study, the authors release this unpractical constraint by assuming that the transmitter in slot 1 and receiver in slot 2 can be any nodes, which are not necessarily being the same. For this scenario, a novel transmission protocol exploiting the overhearing link to suppress the interference caused by asymmetric traffic, denoted as overhearing transmission, is proposed. With the overhearing transmission protocol, and in the light of green communications, the precoding matrices at the decode-and-forward multi-antenna relay are optimised to improve energy efficiency in both uplink and downlink (DL) transmission directions, where the objective is to minimise the transmit power at the relay while guaranteeing a target transmission rate. The authors transform the original non-convex problem to an equivalent form, which can be readily solved by typical semi-definite relaxation approaches. An efficient algorithm is further proposed to implement the precoding design in practice. Simulation results show that the proposed algorithm is able to minimise the power consumption at the relay, with the minimum rate constraints of both the uplink and DL transmissions being satisfied.