  We generalized a class of non-Hermitian Hamiltonians which introduced
previously by us in such a way in which every member in the class is
non-\textit{PT}-symmetric. For every member of the class, the ground state is a
constant with zero energy eigen value. Instead of using an infinite set of
coupled operator equations to calculate the metric operator we used a simple
realization to obtain the class of closed form metric operators corresponding
to the class of non-Hermitian and non-\textit{PT}-symmetric Hamiltonians
introduced. The trick is that, if $\psi$ is an eigen function of $H$, then
$\phi=\eta\psi$ is an eigen function of $H^{\dagger}$ with the same eigen
value. Thus, knowing any pair $(\psi ,\phi)$ one can deduce the form of the
exact metric operator. We note that, the class of Hamiltonians generalized in
this work has the form of that of imaginary magnetic field which can be
absorbed by the quasi-gauge transformations represented by metric operators.
Accordingly, it is expected that the $Q$ operators will disappear for the whole
members in the class in the path integral formulation. However, the detailed
analysis of this issue will appear in another work.
