For a given rational function G{z), analytic outside the closed unit disc and satisfying G(∞) = 0, a new method is proposed for the realization of G by a discrete linear system which is balanced (i.e. its controllability and observability gramians are equal and diagonal). The main numerical steps are the evaluation of a polynomial in a companion matrix, a Cholesky decomposition and a singular-value decomposition. The construction depends on properties of model operators—that is, compressions of the shift operator on the Hardy space H2.