Interference alignment (IA) is a method to improve the capacity of cell-edge users and thus attracts an intense research interest. We focus on the IA extended to the multiple-input multiple-output (MIMO) interference network. In this method, each coordinated transmitter generates beamforming vectors to align interference from different transmitters into confined subspace at each receiver. Then, using singular value decomposition (SVD) with the relative magnitude coefficients, transmitters calculate the beamforming vectors and the received vectors. However, in this method it is difficult to determine the value of the relative magnitude coefficients so that the system capacity is improved, because it is necessary to solve the non-linear function of multivariable. In this paper, we propose a design method of the relative magnitude coefficients of interference channels to improve system capacity using Brent's method on the K-User MIMO interference channel (MIMO-IFC). The proposed method can improve system capacity, though the system complexity increases due to Brent's method that requires multiple SVD calculation to calculate the null space. Thus, instead of using SVD, we introduce the complexity reduction method to calculate the null space of the matrix. Furthermore, we extend the proposed method to be applicable for more common systems where all base stations have the same number of transmit antennas. Through simulation, we show that the proposed method achieves a higher system capacity than the conventional one. We also show that the method that calculates the null space needs much lower complexity than SVD. In addition, we show that the proposed design method reduces the degradation of the system capacity caused by the interference not eliminated, and achieves the fairness of capacities among users for an increase of the number of design coefficients.