Current dual-frequency methods of ionospheric correction eliminate the first order ionospheric term. However, the second and third order ionospheric terms in the refractive index, and errors due to bending of the signal are not fully compensated in this approach. The total electron content is assumed to be the same along two GPS signals, whereas in real cases, due to the dispersive nature of the ionosphere, the TEC along the GPS-L1 path will be different from that along the GPS-L2 path. Although the second order ionospheric term is considered in recent investigations, a common practice is to compute the magnetic field vector at a single point called the ionospheric pierce point assuming the ionosphere as a single layer at a certain altitude. All these approximations lead to erroneous estimations and corrections of the ionospheric errors. In this work, higher order ionospheric errors are rigorously treated and computed for a large number of ionosphere electron density profiles reconstructed from the CHAMP-GPS radio occultation measurements. Different higher order correction formulas have been evaluated using the CHAMP based profiles.