  We discuss a PT-symmetric Hamiltonian with complex eigenvalues. It is based
on the dimensionless Schr\"{o}dinger equation for a particle in a square box
with the PT-symmetric potential $V(x,y)=iaxy$. Perturbation theory clearly
shows that some of the eigenvalues are complex for sufficiently small values of
$|a|$. Point-group symmetry proves useful to guess if some of the eigenvalues
may already be complex for all values of the coupling constant. We confirm
those conclusions by means of an accurate numerical calculation based on the
diagonalization method. On the other hand, the Schr\"odinger equation with the
potential $V(x,y)=iaxy^{2}$ exhibits real eigenvalues for sufficiently small
values of $|a|$. Point group symmetry suggests that PT-symmetry may be broken
in the former case and unbroken in the latter one.
