We calculate the scattering rate of a test electron, due to the Auger process between Landau levels, for two-dimensional electrons in a random potential. The random potential is assumed to be smooth, and its correlation length is large compared to the magnetic length. Two Auger processes were considered. The first one is the Auger process in which two photoelectrons in the same Landau level are scattered, deexciting one to a lower level, losing energy, and exciting the second to a higher level, gaining energy. The second Auger process is the inverse one. In that case a photoelectron from an upper level and a thermal electron from a lower level are scattered, and both are transferred to the same intermediate level. It is shown that the scattering rate is largest for those Auger transitions in which the change in the Landau-level number is equal to 1. The dependence of the scattering rate on the test electron energy and the magnetic field are discussed. As an example, the Auger process in which the interacting electrons are in the second Landau level is considered. Numerical results of the dependence of the Auger scattering rate on the test electron energy and the magnetic field for this case are presented. Simplified formulas for the scattering rate are also suggested.