To achieve signiﬁcant throughput, interference alignment (IA) is an encouraging technique for wireless interference networks. In this study, we design an aligned beamformer based on the interference leakage minimization (ILM) method to reduce the interference power for a multiple-input multiple-output interference channel (MIMO-IC). To deal with the non-convexity of ILM problem, we used a non-convex programming method (i.e., difference of convex [DC]). In this way, the interference leakage function is reformulated to a DC function including difference of two convex terms. Then, an additive function is defined that includes the DC objective function and a penalty function. We propose a novel DC-based IA algorithm that uses solutions of an upper bound of the additive function in each iteration; as the initial state for the next iteration. Through an iterative manner and for the large values of the penalty factor, the solutions of upper bound function converge to the solutions of the original DC objective function (i.e., interference leakage function). In contrast to the frequent IA methods, the proposed DC-based IA algorithm updates transmit- and receive-beamformers in each iteration jointly (not alternately). Simulation results indicate that the proposed method outperforms some competitive IA algorithms by providing more throughputs and less interference leakage.