A general algorithm is presented for the identification of the parameters in the transfer-function matrix of a multi-input—multi-output (MIMO) system. The approach adopted is that of expanding the system input and output variables in shifted Legendre series. The feasibility of the method lies in the generation of linear algebraic equations in the unknown parameters and initial conditions by means of an elegant operational matrix which relates shifted Legendre polynomials to their integrals. An example is included to illustrate the applicability of the proposed method.