Elimination of the ionospheric contribution to atmospheric delays in GPS radio occultation measurements is a key issue in the retrieval of accurate pressure and temperature profiles above the tropopause. The traditional so-called ionosphere-free combination of the L1 and L2 phase paths, eliminating the first-order ionospheric effects, is not sufficient because of the nonnegligible bending of the two ray paths. Because of the dispersive nature of the ionosphere the L1 and L2 signals will follow slightly different paths, giving rise to an ionospheric residual, in this paper referred to as the dispersion residual. Other higher-order ionospheric effects contribute to the total residual, but the dispersion residual is the most dominant. A linear combination of the L1 and L2 bending angles gives better results in most cases and has in recent years become the method of choice. In this paper a new phase path correction method is presented, dealing with the problem of L1 and L2 ray path separation. Formulas are derived showing how the dispersion residual can be evaluated using measurements of the satellite-to-satellite total electron content. The residuals for various conditions in the ionosphere are estimated numerically and compared to analytic estimates. A mathematical formulation of the difference between this improved phase path correction method and the bending angle correction method is obtained, showing that the two methods are nearly equivalent. ¿ 2000 American Geophysical Union