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This paper proposes a novel two-stage method for the design of a suboptimal model-matching controller in an output feedback closed-loop system (OFCLS) using the concept of squared magnitude function (SMF). A streamlined procedure for selection of a reference model, based on a linear quadratic regulator (LQR) with integral action (LQRI) having optimum values for the elements of the weighting matrices and the degree of interaction is proposed. The degrees of the numerator and denominator polynomials of the elements of the OFCLS transfer function matrix (TFM) are obtained from those of the plant and the chosen controller structure. In the first stage of the controller design, taking the LQRI-based closed-loop system (LCLS) as a reference model, the OFCLS is obtained using the approximate model-matching (AMM) technique based on the SMF concept. The approximation method involves a higher-order approximation for stable multiple-input-multiple-output (MIMO) lower-order systems. In the second stage, controller parameters are obtained using the exact model-matching (EMM) method with information about the OFCLS and plant TFMs. The proposed controller design method outperforms the method presented in the literature on integral squared error index. The simulation and experimental results illustrate the effectiveness of the proposed method.