In a new method of finding propagation constants of waveguide modes, the Fourier transform to wave equation is used. We change the differential equation by the integral one. Then we represent the latter equation in a discrete form and get the eigenvalue (square propagation constants)/eigenvector (the discrete Fourier transform of appropriate fields of waveguide modes) problem. Usage of symmetry for symmetric planar waveguides allows to expand opportunities of the new method essentially: to reduce the time of numerical calculation almost triply without loss of analysis accuracy or improve calculation accuracy.