A new technique of identification of linear stationary multi-variable systems is presented in this paper. The natural modes are determined accurately by a Gram matrix formulation of the output functions and the weightings of these modes are calculated by the schemes described. The state equations developed from the decomposed outputs provide, up to a linear equivalence upon the state space, a true description of the system. Among the advantages of the method are its relative insensitivity to noise in the data, and the explicit determination of the system order.