An Improved RGF Method to Find Saddle Points MICHAEL HIRSCH, WOLFGANG QUAPP Mathematisches Institut, Universit"at Leipzig, Augustus-Platz, D-04109 Leipzig, Germany abstract The predictor-corrector method for following a reduced gradient (RGF) to determine saddle points [J.Comput.Chem. {\bf 19} (1998) {1087}] is further accelerated by a modification allowing an implied corrector step per predictor but almost without additional costs. The stability and robustness of the RGF method is improved and the new version in addition reduces the number of gradient and Hessian calculations.