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In this letter, we address the problem of transceiver design in a non-regenerative MIMO relay system, where linear processing is applied at both the relay and destination to jointly minimize the mean-squared error (MSE) of symbol estimations. Under average power constraint at the relay station, we show that the optimal relay-precoder always loads power across channel eigenvectors and then decomposes the equivalent MIMO channel into a set of parallel SISO channels. Simulation results demonstrate that our method outperforms other relaying schemes in terms of both BER and MSE.