In this paper, we investigate the minimum mean squared error based relay transceiver design in amplify-and-forward multiple antenna relay systems in the presence of direct link. Instead of the conventional optimal design which requires iterative methods, we propose a simple and near optimal closed-form solution. The proposed method exploits the decomposable property of the error covariance matrix to simplify the problem. Then, we impose a structural constraint on the non-convex problem to attain a simple closed-form solution. Through numerical simulations, we confirm that the proposed solution has almost no performance loss compared to the optimal iterative design with much reduced complexity.