Abstract In this paper, a new parametrization of all stable multivariable systems satisfying a given bound on their H ∞ norm is presented. This parametrization extends previous results in the sense that it uses a minimum amount of parameters and that it comprises also proper systems. The parametrization has a number of parameters similar to that of classical multivariable state-space forms. The construction of the parametrization is based on the bounded real lemma and the reduction to Hessenberg form by unitary similarity transformations. The parametrization can be used to select the free parameters in a class of all H ∞ controllers in order to include regulation constraints.