  We show that the quasi-exactly solvable eigenvalues of the Schr\"odinger
equation for the PT-invariant potential $V(x) = -(\zeta \cosh 2x -iM)^2$ are
complex conjugate pairs in case the parameter M is an even integer while they
are real in case M is an odd integer. We also show that whereas the PT symmetry
is spontaneously broken in the former case, it is unbroken in the latter case.
