Energies and wave functions of edge states in a two-dimensional electron gas are evaluated for a finite step potential barrier model. The spectrum, instead of smooth bending of Landau branches in the vicinity of the barrier acquires a step-like form; unexpected edge plateaus and significant energy gap reduction take place between the neighbouring Landau branches above the barrier tops. The origin of these phenomena is traced. Stability with respect to modifications is established. Manifestation of the qualitatively new features of electron densities of states in abrupt confinements through magnetooptical and nuclear magnetic spin relaxation effects is proposed.