Previous results on the reduction of single-input/single-output systems are extended to the case of square invertible multivariable systems. It is shown that such systems have a unique decomposition in the form of a forward and a feedback path each having special properties relating to the invariant zeros of the original system. Under certain generic conditions, this decomposition can be extended to yield a representation of the system as a nested sequence of feedback ioops. This provides a convenient method of deriving reduced-order models, which will give good matching of the asymptotic system root locus and open-and closed-loop system dynamics, and hence will be a valid tool in closed-loop controller design.