A proposed mechanism for the generation of gamma ray flashes in the atmosphere, observed on Compton Gamma Ray Observatory satellite, is a runaway discharge mediated by whistler waves. In this model the relativistic electrons produced by a cosmic ray shower during a thunderstorm lead to a runaway discharge, which is maintained by the interaction with whistler waves and the relativistic electrons propagate up in ducts produced by the self-focusing of these waves. The paper presents a detailed study of the instability which develops in the lower stratosphere when a beam of hot magnetized electrons interacts with whistler waves. It was shown that the growth rate of such instability depends on the number density of hot electrons and on their collision rate, and it peaks at about 25 km. The instability develops under the conditions for runaway breakdown, similar to those leading to the generation of strong narrow bipolar pulses, which indicates a possible correlation between these two phenomena.