  We consider rotational hypersurfaces in the $n$-dimensional Euclidean space
${\mathbb{E}}^{n}$. We study the Gauss map $\mathbf{G}$ of rotational
hypersurface in ${\mathbb{E}}^{n}$ with respect to the operator $L_{k}$ acting
on the functions defined on the hypersurfaces with some integers $k=n-3,$
$n\geq 3$. We obtain the classification theorem with Gauss map $ \mathbf{G}$
satisfying $L_{n-3}\mathbf{G}=\mathbf{AG}$ for some $n\times n$ matrix
$\mathbf{A}$.
