  We construct localized beams that are located at the edge of a non-Hermitian
Glauber Fock (NGF) lattice made of coupled waveguides and can propagate for a
long distance without almost no diffraction. Specifically, we calculate the
closed-form of the eigenstates at the exceptional point of a semi-infinite NGF
lattice composed of waveguides which are coupled in a unidirectional manner. We
use the closed-form solution to construct the non-diffracting beams in finite
NGF lattices. We provide a numerical approach to find other lattices that are
capable of supporting non-diffracting beams at an exceptional point.
