  The process of identifying a Dirichlet-type space $D(\mu)$ for a positive,
Borel measure $\mu$, supported on the unit circle $\mathbb T,$ with a de
Branges-Rovnyak space was initiated by Sarason. A characterization of the
symbol for a de Branges-Rovnyak spaces for which the shift operator is a
$2$-isometry, was provided in an article by Kellay and Zarrabi. In this paper,
capitalizing on the Aleman's model for the cyclic, analytic, completely
hyperexpansive operators, we provide a characterization of cyclic, analytic,
completely hyperexpansive operator with finite rank defect operator in terms of
the symbol for a de Branges-Rovnyak space.
