We propose what we believe is a novel method for enabling the complete suppression of noise due to Rayleigh scattering in sodium laser guide star systems by means of selective discrimination between Rayleigh and fluorescence signals based on polarization properties. We show that, contrary to the nearly 100% polarized Rayleigh scattering, fluorescence from the D2 sodium line is strongly depolarized under excitation by a modeless laser. This offers the possibility of completely cancelling the effects of the Rayleigh scattering background while preserving the fluorescence signal to about 40% of its maximal value, leading to an improvement of the signal-to-noise ratio by several orders of magnitude. Both theoretical and experimental data confirm this new proposal.