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A new form of the coprime polynomial fraction $C\left(s\right)F{\left(s\right)}^{-1}$ of a transfer function matrix $G\left(s\right)$ is presented where the polynomial matrices $C\left(s\right)$ and $F\left(s\right)$ 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 $HB$, $HAB$, ...