The methods of processing radio occultation data in multipath zones which were used up to now have very strong restrictions of the applicability. In this paper, we introduce a new approach to the problem of deciphering the ray structure of wave fields in multipath zones using the short-wave asymptotic solution of the wave problem. In geometric optics a canonical transform resolves multipath by introducing new coordinate and momentum in such a way that different rays are distinguished by their coordinates. The wave field is processed by a Fourier integral operator associated with the canonical transform. The transformed wave function can then be written in the single-ray approximation, which allows for the determination of refraction angles from the derivative of the eikonal. The new method retains all the advantages of the back propagation such as the removal of effects of diffraction in free space and the enhancement of the vertical resolution in retrieved profiles, but it has much wider applicability limits. The method is convenient for operational applications. We discuss a fast numerical implementation of the method and present the results of numerical simulations confirming the applicability of the method.