[en] In connection with the experiments on sounding magnetosphere from the Earth surface by very low-irequency signals and investigations of regularities of these waves propagation in magnetosphere thermal modulation instability of whistlers is analytically investigated. The expressions are obtained for instability increment and interval of wave numbers of low-frequency plasma density disturbance at which instability is developed is determined. Threshold frequency values of electron collisions and whistler amplitude are determined. It follows from magnetospheric plasma estimations that the thermal helicon modulation can develop in it at real amplitude values of whistler (H⁰ approximately 10^-₇ epsilon), the wave length of low-frequency disturbance is of the order or more than the electron free path length in plasma. By numerical methods the problem on whistler decay into two satellites and the low-irequency disturbance are investigated