The instability of a low-voltage beam discharge in rare gases is studied using He as an example. Attenuation of an electron beam due to collisions of electrons with atoms is taken into account when the electron mean free path is of the order of the inter-electrode distance. It was found that amplification of several waves with different increments and different speeds is possible with the loss of stability. In the case of a linear decrease in the beam intensity, two waves are generated. The wave having a smaller gain increment propagates at a higher speed. The indicated phenomenon is characteristic not only for a low-voltage beam discharge in rare gases, but also for any "cold high-energy electron beam - plasma"system when collisions of beam electrons with atoms should be taken into account.