We propose a method and an algorithm for recovery of the nonmonotonic altitude profile of the plasma frequency using the model data on oblique sounding of a spherically layered isotropic ionosphere in the piecewise-quasiparabolic approximation of the altitude profile of the electron number density. The algorithm has been tested with a fairly complex ionosphere model allowing for the E, F1 ,a ndF2 layers and the E–F1 interlayer valley. This method was used to recover the effective altitude profile of the plasma frequency at the midpoints of the Khabarovsk–Tory, Magadan–Tory, Norilsk–Tory, and Usolie–Tory paths from the experimental ionograms having a gap in the single-hop mode traces. Recovery of the altitude distribution of the electron number density from oblique ionospheric sounding data yields the main parameters of the ionosphere in a region away from the transmitter and the receiver where the vertical sounding tools are absent for some reasons. Formulation of the problem for a spherically layered isotropic ionosphere makes it necessary to solve a system of two integral equations for the distance between the corresponding points and a range–frequency characteristic (RFC). The desired quantities in this system of equations are the altitude profile of the plasma frequency and the frequency dependence of the arrival (exit) angle of the beam. For the monotonic profiles (without gaps in the RFC), the problem is correct and has a unique solution. For the nonmonotonic profiles (with gaps in the RFC), the problem becomes ill-posed since one RFC can satisfy a family of altitude profiles of the plasma frequency differing in depth of the valley in the profile. Even for the inhomogeneous paths with a nonmonotonic altitude distribution of the electron number density there is a family of media that are only weakly discernible in the oblique ionospheric sounding data [1]. The inverse problem of oblique ionospheric sounding has been studied by many authors. In [2], as the method of solution, the author suggested that the system of integral equations should be reduced to a system of linear equations by a piecewise-parabolic approximation of a monotonic altitude profile of the electron number density. The considered method was improved in [3, 4]. In this approach, the nonmonotonic profiles of the electron number density can be recovered by using a piecewise-parabolic approximation of the plasma frequency squared. This technique was used in the calculations in [5], but there only the accuracy of recovery of a monotonic profile of the electron number density was improved compared with the algorithm based on a piecewise-hyperbolic approximation. In the study [6] based on the oblique ionospheric sounding data, a method is proposed for recovery of the electron number density with small horizontal gradients using the solution of a system of integral equations, but again only for a monotonic altitude profile of the plasma