  New non Hermitian Hamiltonians are generated, as isospectral partners of the
generalized Swanson model, viz., $ H_- = {\cal{A}}^{\dagger} {\cal{A}} + \alpha
{\cal{A}} ^2 + \beta {\cal{A}}^{\dagger 2} $, where $ \alpha \beta $ are real
constants, with $ \alpha \neq \beta $, and ${\cal{A}}^{\dagger}$ and
${\cal{A}}$ are generalized creation and annihilation operators. It is shown
that the initial Hamiltonian $H_-$, and its partner $H_+$, are related by
pseudo supersymmetry, and they share all the eigen energies except for the
ground state. This pseudo supersymmetric extension enlarges the class of non
Hermitian Hamiltonians $H_{\pm}$, related to their respective Hermitian
counterparts $h_{\pm}$, through the same similarity transformation operator
$\rho$ : $ H_{\pm} = \rho ^{-1} h_{\pm} \rho $. The formalism is applied to the
entire class of shape-invariant models.
