The novel Multiple-Branching Classical Trajectory Surface-Hopping Method is derived for treating multi-dimensional nonadiabatic nuclear dynamics. The method is applied to the radiationless decay process of the ammonia cation after photoionization of the neutral ammonia molecule. It is shown that the mechanism of the process is based on nonadiabatic transitions in the vicinity of conical intersections. The femtosecond time-dependent adiabatic populations for different electronic states of the ammonia cation are calculated and compared with the results of the quantum calculations.