High order nonlinear characteristics of electromagnetically induced transparency (EIT) media are theoretically investigated, and a new theoretical method different from iterative method is introduced based on the distribution of dark resonance and leading to a complete solution for a density matrix element. From the solution, every order response for atoms to the probe field is obtained. It is demonstrated that the linear susceptibility (first order) shows destructive interference while the nonlinear susceptibility (third order) displays instructive interference. The even-order nonlinearity is absent in an isotropic medium. Furthermore, it shows that the fifth order nonlinear susceptibility exhibits destructive interference as the linear susceptibility. These research results provide an theoretical foundation for investigating, for example, the evolution of optical wave under high order nonlinearity in an EIT medium. The new method provides a novel approach for the study of high order nonlinearity.