  Let $\mathcal{F}$ be a foliation with a "singular" submanifold $B$ on a
smooth manifold $M$ and $p:E \to B$ be a regular neighborhood of $B$ in $M$.
Under certain "homogeneity" assumptions on $\mathcal{F}$ near $B$ we prove that
every leaf preserving diffeomorphism $h$ of $M$ is isotopic via a leaf
preserving isotopy to a diffeomorphism which coincides with some vector bundle
morphism of $E$ near $B$. This result is mutually a foliated and compactly
supported variant of a well known statement that every diffeomorphism $h$ of
$\mathbb{R}^n$ fixing the origin is isotopic to the linear isomorphism induced
by its Jacobi matrix of $h$ at $0$. We also present applications to the
computations of the homotopy type of the group of leaf preserving
diffeomorphisms of $\mathcal{F}$.
