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We propose a new reduced-dimension (RD) eigen-direction alignment (EDA) precoder for MIMO two-way relay channels (TWRCs) with nR >; nT, where nR denotes the number of antennas at the relay, and nT is that at each of the two users. The RD-EDA precoder can efficiently create aligned eigen-modes for the two users, enabling independent streams of physical-layer network coding. We investigate the design of the RD-EDA and develop a simple suboptimal solution. It is shown that the proposed RD-EDA scheme performs close to the sum-capacity upper bound of the MIMO TWRC. Moreover, it is shown that the proposed scheme can significantly outperform other existing schemes in the literature.