Abstract: It is proved that a general coplanar discontinuity can be decomposed according to (这里有图片19980204-119.GIF). Here the arrow over symbol represents the propagation direction of the related outcome of decomposition, J represents the contact surface, W_f is the fast-mode wave, containing the fast shock, fast simple wave, intermediate shock of type 1→3, and the first kind of fast compound wave, and W_s is the slow-mode wave,containing the slow shock, slow simple wave, intermediate shock of type 2→4, and the first kind of slow compound wave. The decomposition of several specific discontinuities is also discussed.