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The whistler instability is studied under the condition that the electron and ion velocities can be described in a bi-Maxwellian distribution with a field-aligned electron outflow drift velocity. It is found that the electron outflow drift velocity might obviously make the threshold condition of whistler instability decrease when this velocity is parallel to the magnetic field, whereas the electron outflow drift velocity might increase the threshold condition when this velocity is anti-parallel to the magnetic field in collisionless magnetic reconnection.