In this paper the method suggested by L. A. P. Balazs for solving the problem of the low energy pion-pion scattering is applied to the kaon-pion scattering process. It isfound that the position of the K* resonance is (SR)1/2=854MeV, the half-width 1/2Г11/2 = 126 MeV, and the phenomenological constant of the amplitude of the process π + π→ K + K ξ = 0.3 μ-2. The position of the K* resonance is in good agreement with experiment.