In this letter, a precoding design for a multiple-input multiple-output (MIMO) full-duplex relay (FDR) system is proposed. For this system, mitigating the self-interference imposed by the transmit antennas on the receive antennas in the same relay station is crucial for improving the performance of the FDR system. The precoding scheme designed in this study uses block-diagonalization (BD). Using this precoding scheme, FDR capacity analysis is performed in the MIMO downlink relay system. Numerical results on system performance in terms of capacity are shown and discussed.