The filainentation instability of whistler waves in the magnetosphere is analyzed in this paper, and the growth nate is calculated. For propagation path L = 4 and electric field of the wave 1 mV/m, the maximum growth rate is about 0.13/1000 km, the corresponding perpendicular wave length is about 400 km (near the equator region). It is also pointed out that the filaxnentation instability discussed here may offer a nonlinear mechanism for the multi-path propagation of whistlers.