A theoretical and algorithmic framework is proposed for the identification of rational transfer function matrices of a class of discrete-time multivariable systems. The proposed technique obtains an optimal approximation from the given (possibly noisy) measured impulse response data. It is assumed that the measured impulse response data corresponds to a system with a strictly proper transfer function matrix. The impulse response fitting error criterion is theoretically decoupled into a purely linear problem for estimating the optimal numerators and a nonlinear problem for the optimal denominators. Based on the proposed theoretical basis, an efficient computational algorithm is developed and illustrated with several examples. © 1994 Birkhäuser.