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In multi-cell communication, users close to the cell boundaries tend to suffer interferences from other-cell users. Other-Cell Interference (OCI) coming from neighbouring cells considerably degrades the overall performance of the system. In this paper, we propose a precoding scheme for the multi-user multi-input multi-output (MIMO) downlink based on the regularized channel inversion algorithm to mitigate the effect of OCI in multi-cell systems. The scheme is designed by taking into account the interference plus noise covariance matrix of each user at the transmitter and the use of an interference suppression filter at each receiver. Unlike traditional OCI-aware Block Diagonalization (BD) based algorithms that experience noise enhancement due to complete elimination of multi-user interference (MUI), this scheme suppresses the MUI while taking the OCI into consideration. Simulation results show that the sum-rate performance of the proposed scheme outperforms the OCI-aware BD algorithm for different OCI settings.