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A numerical method of fitting a multiparameter function, non-linear in the parameters which are to be estimated, to the experimental data in the $L_1$ norm (i.e., by minimizing the sum of absolute values of errors of the experimental data) has been developed. This method starts with the least squares solution for the function and then minimizes the expression ${\sum }_i{(x_i^2+a^2)}^{1/2}$, where $x_i$ is the error of the $i$-th experimental datum, starting with an $a$ comparable with the root-mean-square error of the least squares solution...