An expansion procedure to design partially decentralized controllers was recently proposed. This method requires the operation of pseudo-inverse of non-square matrices, which is not unique. Thus, it introduces an extra design freedom, which was not addressed in the previous studies. In this paper, the effect of the pseudo-inverse on the stability and performance of 2 x 2 partially decentralized control systems is studied. Specifically, the range of the pseudo-inverse factors arising from the stability condition of the control system is derived. In addition, an 'ideal' pseudo-inverse factor, which minimizes interaction in the control system, is obtained based on the concept of non-square block relative gain. Simulation results show that a partially decentralized controller with the 'ideal' pseudoinverse factor gives an improved controller performance.