The problem of diffraction of a normally incident plane wave by a wedge with thin material coatings is studied. The thin coatings are simulated by the generalized impedance boundary conditions of the third order. At the points of junction of the coatings, that is, on the edge of the wedge, additional constraints are formulated. These constraints, or contact conditions, ensure uniqueness of the solution in the diffraction problem. The solution is determined in an explicit form by means of the Maliuzhinets' technique. The uniform and local asymptotics of the far field are deduced.