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In this paper, we study the performance of the training based two-step channel estimation in two-way multiple-input multiple-output relay systems over Rayleigh channels. We first estimate the forward channel during the first phase. During the second phase for the composite channel estimation, singular value decomposition based maximum likelihood method is applied in two way relay systems, which is extended from one way relay systems. Hence, the backward channel is estimated with the given forward channel and composite channel. In general, the proposed estimation scheme can also be extended from the system with a single relay antenna to multiple relay antennas. Moreover, we derive the proposed training sequences and relay gain that aim to minimizes the trace of the approximate Bayesian Cramér–Rao lower bound with respect to the individual channels. The numerical results are shown that although the training sequence is designed to improve individual channel mean square error performance, it can also improve composite channel estimator performance. [ABSTRACT FROM AUTHOR]