A model of the evolution of finite amplitude upper hybrid waves generated at the upper hybrid resonance height during high-power radio wave ionospheric heating is presented. We show that the threshold for modulation instability can be exceeded for upper hybrid wave amplitudes of the order of a few tens of millivolts per meter and will be excited for scale sizes, perpendicular to the geomagnetic field, of the order of a few tens of electron gyroradii. ¿ 1998 American Geophysical Union