A new form of the coprime polynomial fraction $C(s) F(s)^{-1}$ of a transfer function matrix $G(s)$ is presented where the polynomial matrices $C(s)$ and $F(s)$ have the form of a matrix (or generalized matrix) polynomials with the structure defined directly by the controllability characteristics of a state-space model and Markov matrices $HB$, $HAB$, \ldots