  We establish a connection between an arbitrary Hermitian tight-binding model
with chiral (C) symmetry and its non-Hermitian counterpart with chiral-time (CT
) symmetry.We show that such a non-Hermitian Hamiltonian is pseudo-Hermitian.
The eigenvalues and eigenvectors of the non-Hermitian Hamiltonian can be easily
obtained from those of its parent Hermitian Hamiltonian. It provides a way to
generate a class of non-Hermitian models with a tunable full real band
structure by means of additional imaginary potentials.We also present an
illustrative example that could achieve a cone structure from the energy band
of a two-layer Hermitian square lattice model.
