Consider a nearest-neighbor random walk on two-dimensional lattice confined to an angle $\pi/4$ (an eight-plane), with boundary conditions on the border lines. Assume that the walk is homogeneous inside the angle and along the border lines. Under the conditions that the walk is positive recurrent, what is the asymptotical behavior of the equilibrium probabilities? This problem was studied by V. Malyshev and co-workers for a quarter-plane and has important applications. In the talk I'll show how Malyshev's approach can be modified to cover the case of the eight-plane. The talk will not require any knowldedge of special character.