  A method to construct non-dissipative non-Dirac-hermitian relativistic
quantum system that is isospectral with a Dirac-hermitian Hamiltonian is
presented. The general technique involves a realization of the basic canonical
(anti-)commutation relations involving the Dirac matrices and the bosonic
degrees of freedom in terms of non-Dirac-hermitian operators, which are
hermitian in a Hilbert space that is endowed with a pre-determined
positive-definite metric. Several examples of exactly solvable non-dissipative
non-Dirac-hermitian relativistic quantum systems are presented by
establishing/employing a connection between Dirac equation and supersymmetry
