[en] A new method of inversion of the S-wave scattering amplitude based on the Schwinger variational method is presented. This method is accurate and stable and is applicable to a number of interesting physical systems such as nucleon-nucleon or nucleon-nucleus scattering even when the data are known for a finite nonrelativistic range of energies. Examples of different scattering amplitudes and their corresponding potential functions are given to show the accuracy and the stability of the method. (Author) 10 refs., 5 figs., 3 tabs