  We study the connection between a family of non-Hermitian Hamiltonians H and
Hermitian ones H based on exact solutions. In general, for a dynamic process in
a non-Hermitian system H, there always exists a parallel dynamic process
governed by the corresponding Hermitian conjugate Hamiltonian H{\dag}. We show
that a linear superposition of the two parallel dynamics is exactly equivalent
to the time evolution of a state under a Hermitian Hamiltonian H. It reveals a
novel connection between non-Hermitian and Hermitian systems.
