In the plane wave scattering from a periodic grating high order diffracted plane waves disappear at a low grazing angle limit of incidence. In this paper the scattering of a beam wave by the end-face of an ordered waveguide system composed of identical cores of equal space is treated by the perturbation method and the scattered field is analytically derived. The possibility that high order diffracted beam waves remain at a low grazing angle limit of incidence is shown.