It is shown that quasi-monochromatic whistler waves (wavelets) can be caused by the strong cyclotron instability, stimulated by hiss emissions. The hiss, generated by the cyclotron instability of an anisotropic smooth energetic electron distribution, creates a step-like deformation of the distribution function at the boundary between resonant and nonresonant electrons. This deformation leads to the strong amplification of the wavelet whose frequency corresponds to that for cyclotron resonance with electrons at the step. Analytical calculations for this amplification have been made using the rigorous theory of the cyclotron instability in an inhomogeneous magnetic field. The wave amplification can be 2 orders of magnitude greater than that for a smooth distribution function. A self-consistent computational analysis of the cyclotron instability is developed on the basis of quasi-linear theory. This confirms both the formation of the step-like deformation of the distribution function and the wavelet generation. ¿ American Geophysical Union 1996