  The pentablock is a Hartogs domain over the symmetrized bidisc. The domain is
a bounded inhomogeneous pseudoconvex domain, and does not have a
$\mathcal{C}^{1}$ boundary. Recently, Agler-Lykova-Young constructed a special
subgroup of the group of holomorphic automorphisms of the pentablock, and
Kosi\'nski completely described the group of holomorphic automorphisms of the
pentablock. The purpose of this paper is to prove that any proper holomorphic
self-mapping of the pentablock must be an automorphism.
