  Hill-determinant method is described and shown applicable within the so
called PT-symmetric quantum mechanics. We demonstrate that in a way paralleling
its traditional Hermitian applications and proofs the method guarantees the
necessary asymptotic decrease of wave functions as resulting from a fine-tuned
mutual cancellation of their asymptotically growing exponential components.
Technically, the rigorous proof is needed/offered that in a quasi-variational
spirit the method allows us to work, in its numerical implementations, with a
sequence of truncated forms of the rigorous Hill-determinant power series for
the normalizable bound states.
