A new version of asymptotically exact theory of spectrum and transverse distribution of magnetization in long-wave magnons is presented. It is based on exact analytical solution of the linearized Landau-Lifshitz equation in a film. We also studied and used symmetry of the Hamiltonian. Our method simplifies all calculations and allows us to obtain analytical results for the range of parameters most important for experiment. The quantization of the transverse wave vector and role of evanescent waves at different values of parameters are studied.