Radio occultation sensing of the terrestrial atmosphere can be performed by using signals from Global Positioning System (GPS) or Global Navigation Satellite System (GLONASS) satellites, which are received by satellites in low Earth orbit. The signal transmitted from a GPS/GLONASS satellite, when occulted, suffers propagation effects in the ionosphere and atmosphere, including carrier and group phase shifts and ray path bending. Those propagation effects give direct information on the refractivity of the medium of occultation. In order to sense the neutral atmosphere only, we have to carefully correct for the ionospheric contribution to the propagation effects whose influences are poorly known at present time. In this paper, we provide a straightforward method for model-independent correction of the ionospheric effects based on the correction of the ionospheric bending angle rather than correction of the optical path lengths, as done by previous studies. Using the presented correction, the accuracy of retrieved temperature profiles of the atmosphere is better than 1 K up to heights of some 55 km during typical ionospheric conditions. The formalism can easily be implemented in on-line analyses of phase data obtained by the radio occultation technique. This promising technique may thus in fact become an extremely valuable tool for supporting climate monitoring as well as weather and climate modeling and prediction.