  An example of exceptional points in the continuous spectrum of a real,
pseudo-Hermitian Hamiltonian of von Neumann-Wigner type is presented and
discussed. Remarkably, these exceptional points are associated with a double
pole in the normalization factor of the Jost eigenfunctions normalized to unit
flux at infinity. At the exceptional points, the two unnormalized Jost
eigenfunctions are no longer linearly independent but coalesce to give rise to
two Jordan cycles of generalized bound state eigenfunctions embedded in the
continuum and a Jordan block representation of the Hamiltonian. The regular
scattering eigenfunction vanishes at the exceptional point and the irregular
scattering eigenfunction has a double pole at that point. In consequence, the
time evolution of the regular scattering eigenfunction is unitary, while the
time evolution of the irregular scattering eigenfunction is pseudounitary. The
scattering matrix is a regular analytical function of the wave number $k$ for
all $k$ including the exceptional points.
