Temperature, pressure, and humidity profiles of the Earth's atmosphere can be derived through the radio occultation technique. This technique is based on the Doppler shift imposed, by the atmosphere, on a signal emitted from a GNSS satellite and received by a low orbiting satellite. The method is very accurate with a temperature accuracy of 1°K, when both frequencies in the GPS system are used. However, difficulties arise when the signal consists of multiple frequencies generated by multipath phenomena in the atmosphere. We demonstrate that, in general, it is possible to determine the arrival times of the different frequency components in a radio occultation signal simply as the derivatives of the phases of the conjugated Fourier spectrum of the entire occultation signal. Based on this property, a novel Full Spectrum Inversion technique for radio occultation sounding capable of disentangling multiple rays in multipath regions is presented. As the entire signal is used in the Fourier transform, a high spatial resolution in the Doppler frequency, and hence in the retrieved temperature, pressure, and humidity profiles, can be achieved. The method is conceptual and computational simple and thus easy to implement. The performance of the Full Spectrum Inversion is demonstrated by applying the technique to simulated signals generated by solving Helmholtz equation with use of the multiple phase-screen technique. Excellent agreement is found between computed bending angle profiles and corresponding solutions to the Abel integral.