It is considered the transition radiation when the charged particle crosses the boundary of plasma medium, in the cases of uniform motion and the motion, which consists of two parts of uniform motion, with two running across the boundary. The solution of the problem is obtained for the conditions when the spatial dispersion is large, skin effect is anomalous, and the reflection of the electrons from the boundary is partially specular and partially diffuse. There are found the differences of characteristics of radiation from ones available in the case of ideally conducting medium and the conditions, for which these differences are considerable. It is considered the question about effectiveness of generation of wide band radiation with use of pulsed accelerators.