Using a Green's function method of approximation, transmission and reflection coefficients are computed for the problem of Rayleigh waves normally incident upon the corner of a homogeneous elastic wedge formed by two stress-free planes. The Rayleigh waves are incident from infinity and travel along one surface of the wedge. The transmitted waves on the second surface and the reflected waves on the first surface are calculated by the application of Huygens' principle. A pair of coupled integral equations for the displacements are obtained by means of a representation theorem. Neglecting the diffracted body waves near the corner, the coupled integral equations are reduced to a pair of algebraic equations. A new feature of the calculation involves consideration of diffracted surface waves travelling toward the vertex. Numberical values of the phase shifts and attenuation factors in the transmitted and reflected waves are computed as functions of the wedge angle. Comparison with experimental results show considerably better agreement than has been obtained previously.