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Full duplex (FD) multiple-input multiple-output (MIMO) relaying can significantly increase the spectral efficiency of cooperative communication systems. This paper examines the problem of linear source and relay precoder and destination combiner design for two-way MIMO FD amplify-and-forward (AF) relay communication systems. The effect of the residual loop interference (LI) due to imperfect LI cancellation is considered in the design. Two algorithms are proposed to minimize the mean squared error (MSE) of the received signals at the destinations. The first is a tri-step alternating iterative algorithm and the second is a bi-step iterative algorithm. The convergence and complexity of these algorithms are analyzed. Simulation results are presented, which show that the proposed two-way FD system provides approximately double the achievable rate of the corresponding half-duplex (HD) system when the residual LI is low. Furthermore, the bi-step algorithm shows comparable performance to the tri-step algorithm and has a lower computational complexity.