In this work we present an algorithm for solving the inverse problem to reconstruct the parameters of the horizontally (thinly stratified) anisotropic layer. Conditions of symmetry for the trace of the direct problem solution on the surface was used together with usual form of the additional information (value of the direct problem solution on the surface). The numerical solution of the inverse problem was found in the frequency domain. The general statement of the inverse problem was decomposed into the series of the standard inverse problem statements to reconstruct sequentially the available medium parameters. Several numerical experiments are presented.