A new integration technique, symplectic method, is introduced and applied for the tracing of a charged particle motion in a dipole magnetic field. This method is an integral technique for the Hamilton's system by the repetition of canonical transformation, and has been tested in celestial mechanics in recent years. Compared with the standard Runge-Kutta method (4th order), the numerical error accumulation is much smaller for the symplectic method. An effective potential is introduced and used to discuss an abrupt transition between trapping and un-trapping regions. ¿ 2001 American Geophysical Union