Abstract: According the characters of resonance of relativistic particles with electromagnetic waves, the instability of whistler waves produced by relativistic electron beam is studied. The resonant points in momentum space of particles lie in a series of hyperbolas. For a electron beam of lose-cone distribution this resonant phenomenon makes a rising of the threshold of the instability. This rising is effective in frequency band of w-0.5Ω_e and in case e-Ω_e, and it decreases with the increasing of the parameter w_e/w_e.