In this paper, the problem of transceiver design in a non-regenerative MIMO relay system is addressed, where linear signal processing is applied at the relay and destination to minimize the mean-squared error (MSE) of the signal waveform estimation. The optimal structure of the relay precoding matrix is derived with the assumption that the relay knows the channel covariance information of the relay-destination link and the full channel state information (CSI) of the source-relay link. Simulation results demonstrate that the proposed scheme outperforms conventional relay algorithms, and its performance is comparable to the optimal relay algorithm using the full relay-destination CSI.