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GPS radio occultations allow the sounding of the Earth's atmosphere (i.e. troposphere and ionosphere). The basic observable of this technique is the additional delay, due to the refractivity index, of a radio signal when passing through the atmosphere. This additional delay is proportional to the integrated refractivity, in such a way that we can obtain an estimation of the vertical refractivity profiles using observations at different elevation angles by solving an inverse problem. Traditionally, the solution of this inverse problem is obtained by using the Abel inversion algorithm assuming a refractivity index that only depends on the altitude. In this paper we present a modified Abel inversion algorithm for ionospheric sounding that overcomes the spherical symmetry assumption of the traditional Abel inversion algorithm. Processing a set of simulated data and 1 day of real data with this algorithm, a clear improvement over the traditional one can be obtained when comparing the derived critical frequencies with the ionosonde measurements. It is also shown that this improvement is sufficient to measure critical frequencies associated with the ionospheric E layer.