  Discrete PT-symmetric square wells are studied. Their wave functions are
found proportional to classical Tshebyshev polynomials of complex argument. The
compact secular equations for energies are derived giving the real spectra in
certain intervals of non-Hermiticity strengths Z. It is amusing to notice that
although the known square well re-emerges in the usual continuum limit, a twice
as rich, upside-down symmetric spectrum is exhibited by all its present
discretized predecessors.
