A new transport theory method of characteristic direction probabilities (CDP), which can treat complicated geometries with computational efficiency, is presented. In the method, the entire problem is divided into subsystems or cells that are further subdivided into finer mesh regions (i.e., computational meshes). Within a subsystem or cell, the fine meshes are coupled by the directional transmission and collision probabilities for each characteristic direction. In other words, all fine meshes in a subsystem are not coupled together but only the fine meshes along the characteristic line are coupled for each direction. This is in contrast to the traditional collision probability methods (CPMs). To calculate the directional probabilities, ray tracing with the macroband concept is performed only on each subsystem type. To couple the subsystems, the angular flux (not the current as in the interface current method) on the interface between the adjacent subsystems is used. Therefore, the method combines the most desirable features of the discrete ordinates methods and those of the integral transport methods. To verify CDP, it is applied to two benchmark problems that consist of complex meshes and is compared with other methods (CPM, method of characteristics, and Monte Carlo method). The results show that CDP gives accurate results with short computing time.