The Kronecker canonical form is generalized from the set of matrix pencils to the set of all the rational matrix functions \(W(\lambda)=\sum^{\ell}_{i=-\infty}W_ i\lambda^ i\), in a way which depends on the choice of \(\ell \in {\mathbb{N}}\). If a polynomial system \(W(\lambda)=C(\lambda I-A)^{-1}B+\sum^{\ell}_{i=0}W_ i\lambda^ i\) is given as a partial realization for W, the \(\ell\)-Kronecker form of W is shown to be equal to the classical Kronecker form of the companion pencil. This invariance property fails if we replace the Kronecker form by the McMillan canonical form.