We use a combination of the center—Lipschitz condition with the Lipschitz condition condition on the Frechet—derivative of the opera­tor involved to provide a semilocal convergence analysis ofthe Gauss-Newton method to a solution ofan equation. Using more precise esti­mates on the distances involved, under weaker hypotheses, and under the same computational cost, we provide an analysis of the Gauss— Newton method with the following advantages over the corresponding results in [8]: larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location ofthe solution.