In this paper, a relay precoding problem is considered in a non-regenerative multiple-input multiple output (MIMO) relay system, when multiple interferers exist near the destination. The relay has the perfect channel state information (CSI) of the source-relay link and only the covariance information of the relay-destination link. Also, we assume that the training signals of the interferers are known at the destination, and thus, the covariance information of the channels from the interferers to the destination can be estimated at the destination and the information is fed back to the relay. For this scenario, the structure of the optimal relay precoder is derived to maximize the average capacity seen by the relay under a relay transmit power constraint. For the derivation of the optimal relay precoder, a new partial ordering result for the outage probability and the ergodic capacity of spatially correlated MIMO channels is derived. Numerical results demonstrate that the proposed scheme considerably improves the performance. Overall, the contributions of this paper are twofold: i) a new partial ordering result for MIMO channels is derived and ii) the structure of the optimal relay precoder is derived using the partial ordering result.