  The Hermitian systems possess unitary scattering; however, the Hermiticity is
unnecessary for a unitary scattering although the scattering under the
influence of non-Hermiticity is mostly non-unitary. Here we prove that the
unitary scattering is protected by certain type of pseudo-Hermiticity and
unaffected by the degree of non-Hermiticity. The energy conservation is
violated in the scattering process and recovers after scattering. The subsystem
of the pseudo-Hermitian scattering center including only the connection sites
is Hermitian. These findings provide fundamental insights on the unitary
scattering, pseudo-Hermiticity, and energy conservation; and are promising for
the light propagation, mesoscopic electron transport, and quantum interference
in the non-Hermitian systems.
