This paper investigates the interference alignment (IA) solution for a K-user static flat-fading multiple input multiple output (MIMO) interference channel. Optimal users' precoders and postcoders are designed through a rank constraint rank minimization (RCRM) framework with IA conditions inserted within the constraints and the cost function of a complex matrix optimization problem. With RCRM formulation, the interference is forced to span the lowest dimensional subspace possible, under the condition that the useful signal subspaces span all available spatial dimensions. Using the recent advances in matrix completion theory and low rank matrix recovery theory, we propose an Iterative Reweighted Least Squares (IRLS) approach to IA. Through this approach, we provide an adequate relaxation for the rank function which in some cases attain the same results obtained using the standard nuclear norm with lower elapsed time per iteration and lower number of iterations and in some cases perform better than any of the previous approaches.