Interference alignment (IA) techniques raise the achievable degree of freedom (DoF) in wireless interference networks by designing the aligned transceiver beamformers. The DoF shows the number of interference-free data streams that can be communicated simultaneously on a channel. To achieve the maximum possible DoF, we design the aligned beamformers in this study based on the interference leakage minimization (ILM) method for a multiple-input multiple-output interference channel (MIMO-IC). Accordingly, the ILM optimization problem is firstly relaxed to the rank constrained semidefinite programming (SDP) problems. Next, using a non-convex programming method (i.e., the difference of convex [DC] programming method), the proposed non-convex rank constrained SDP problem is reformulated to the DC form. We propose a novel DC-based IA algorithm that designs the optimized aligned beamformers based on an iterated local search using a penalty function. By increasing the penalty factor, the solution of the penalized DC problem converges to the solution of the original DC problem. Unlike the previous IA approaches, the proposed DC-based IA algorithm optimizes transmit and receive beamformers jointly and simultaneously in each iteration (i.e., not alternately). Simulation results indicate that the proposed method outperforms the previous competitive IA algorithms by providing more throughputs and less interference leakage as compared to the least-squares (LS)-based and the minimum mean square error (MMSE)–based IA algorithms.