In this paper, we treat a design problem for IIR digital filters described by rational transfer function in discrete space. First, we form the filter design problem using the modified least-squares (MLS) criterion and express it as the quadratic form with respect to the numerator and denominator coefficients. Next, we show the relaxation method using the Lagrange multiplier method in order to search for the good solution efficiently. Additionally we can check the filter stability when designing the denominator coefficients. Finally, we show the effectiveness of the proposed method using a numerical example.