In the magnetosphere, energetic electrons in the radiation belts are trapped by the Earth's dipole magnetic field and undergo bounce motion about the geomagnetic equator. It is shown that the trajectories of some of the trapped particles can in the presence of a whistler wave become chaotic and wander into the loss cone. Comparing the surface of section plots obtained from the both relativistic equations of motion and from the nonrelativistic ones, the effect of the relativistic correction to the electron motion are shown. The threshold field for the commencement of chaos in the trajectories of electrons with energies of a few hundred keV is found to be lowered by the inclusion of relativistic effects by about an order of magnitude. Waves with these smaller magnetic field amplitudes (about 1% of the geomagnetic field) have been observed propagating between hemispheres. Since this chaotic scattering process does not have a directional preference, it offers a plausible explanation for the simultaneous observation of electron precipitation into the upper atmosphere at geomagnetically conjugate regions because of a single lightning flash [Burgess and Inan, 1990>.¿ 1997 American Geophysical Union