We study an electron in a two-dimensional system of random point scatterers placed on the sites of a regular square lattice subject to a perpendicular magnetic field B. When the energy equals the Landau energy en(B) (n = 0, 1,...) above a certain magnetic field Bn (which corresponds to the presence of n + 1 flux quanta Ph0 = hc/e per an elementary square) we find analytically disorder-independent extended eigenstates.