We present a diffraction coefficient for calculating the field on the surface of a perfectly conducting two-dimensional curved face wedge, illuminated by a TE plane wave. The surface field consists of a geometrical optics (GO) field supplemented by a creeping wave launched by edge diffraction. The GO field is that which would exist on the circular cylinder of which the wedge face is a part, subject to the same illumination. The diffracted field takes the form of a creeping wave and is related to the incident field at the edge by the new diffraction coefficient$Delta$.$Delta$is found by requiring the sum of the diffracted and GO fields to equal the correct field determined by numerical methods in a range of representative cases.$Delta$is found to be a function of distance close to the edge and then becomes constant with increasing distance; thus, our method is valid for all distances from the edge, including zero. We have developed relatively simple analytic expressions for$Delta$as a function of plane wave incidence direction, wedge angle, radius of curvature of the surfaces and distance of the field point from the edge. These expressions have been found to give good prediction of surface magnetic field for cases different from those for which the original data was calculated.