A concise formulation of the uniform geometrical theory of diffraction (UTD) solution for the scattering by a wedge with isotropic impedance faces at a plane wave normally incident case is deduced in this paper, which inherits the uniformity of the original result. It overcomes the complexity of the former, expresses clearly physical meanings, and is very prone to calculation with computer. The numerical results agree well with those given by published papers. A concise formulation of the uniform geometrical theory of diffraction (UTD) solution for the scattering by a wedge with isotropic impedance faces of a plane wave normally incident case is deduced in this paper, which inherits the uniformity of the original result. It overcomes the complexity of the former, expresses clearly physical meanings, and is very prone to calculation with computer. The numerical results agree well with those given by published papers.