  In this paper, a non-trivial system governed by a continuum PT-symmetric
Hamiltonian is discussed. We show that this Hamiltonian is iso-spectral to the
simple harmonic oscillator. We find its eigenfunctions and the path in the
complex plane along which these functions form an orthonormal set. We also find
the hidden symmetry operator, ${\cal C}$, for this system. All calculations are
performed analytically and without approximation.
