The weakly guiding approximation is the basis for the most well-known methods and their extensions for evaluation of
optical waveguide parameters. However, solutions of scalar wave equations are not exact, and there are some applications
requiring more high accuracy. It is obviously, polarization effects, occurred by guiding properties of the optical
fibers, must be taken into account to improve the accuracy. Thus, "polarization correction" term, described by A. Snyder,
must be added to scalar propagation constant. Method, based on Gaussian approximation, for calculation of polarization
correction to the any order mode propagation constant in weakly guiding optical fiber with an arbitrary coaxial index
profile is proposed. Results of error reducing by adding of correction to propagation constant, obtained by scalar wave
analysis, are demonstrated. First and second order derivatives of the correction are obtained and represented.