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In this paper, we propose a design scheme for amplify-and-forward multiple-input multiple-output (AF MIMO) relay system with direct link to minimize the mean-squared error (MSE) of the signal estimation at the destination. In the proposed design scheme, an optimal precoding matrix is derived with the assumption that the full channel state information (CSI) of the source-relay link and partial channel state information such as channel covariance information (CCI) of the relay-destination link are available at the relay. In practical cases, if the destination is closer to the source, the source-destination link cannot be ignored. Hence, in this paper, we assume that the relay knows the partial channel state information of the source-destination link. Based on this assumption, an iterative optimal covariance algorithm is developed to achieve the minimum MSE of the signal estimation at the destination. In order to reduce computational complexity of the proposed optimal covariance algorithm, a suboptimal covariance algorithm is proposed. A numerical example shows that the developed optimal covariance algorithm outperforms the conventional CCI based MSE algorithms.