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We propose a low complexity design of the linear transmit filters for a MIMO interference channel. This design is based on a minimum mean squared error (MMSE) approach incorporating the signal and the interference leakage for each transmitter. Unlike the previous methods, it allows a closed-form expression of the regularization factor for the MMSE transmit filter. Hence, it requires a lower computational complexity compared to the conventional MMSE approach that is optimally achieved by solving a polynomial equation to find the regularization factor. Furthermore, the mean squared error (MSE) performance of the proposed design is verified by simulations to have nearly no loss compared to the conventional MMSE approach.