A new parametrization of the multi-channel S
-matrix is used to fit scattering data and then to locate the resonances as its poles. The S
-matrix is written in terms of the corresponding “in” and “out” Jost matrices which are expanded in the Taylor series of the collision energy E
around an appropriately chosen energy E 0
. In order to do this, the Jost matrices are written in a semi-analytic form where all the factors (involving the channel momenta and Sommerfeld parameters) responsible for their “bad behavior” (i.e., responsible for the multi-valuedness of the Jost matrices and for branching of the Riemann surface of the energy) are given explicitly. The remaining unknown factors in the Jost matrices are analytic and single-valued functions of the variable E
and are defined on a simple energy plane. The expansion is done for these analytic functions and the expansion coefficients are used as the fitting parameters. The method is tested on a two-channel model, using a set of artificially generated data points with typical error bars and a typical random noise in the positions of the points.