Cyclotron instability is studied in a homogeneous plasma with an anisotropic non-Maxwellian ion distribution by velocities and Maxwellian electrons. It is shown that plasma can be unstable at any ratio between mean transverse and mean longitudinal ion energy, if the ion distribution function for the transverse velocities φ (ν/ν0) is a non-monotonous function. The "beam" character of the function φ (ν/ν0) is. in this case the physical cause for appearance of this type of instability. The"quasi-transverse" waves are the most unstable waves, propagating almost perpendicularly to the external magnetic field. Plasma stability improves with the increase of electron temperature. If the mean transverse ion energy is much larger than the longitudinal energy, the effect of nonmonotony of the function φ (ν/ν0) becomes unessential and the results of Ref. 1 remain valid for cyclotron instability.