Central to the theoretical description of a chemical reaction is the reaction pathway. The intrinsic reaction coordinate is defined as the steepest descent path in mass weighted Cartesian coordinates that connects the transition state to reactants and products. In this work, a new integrator for the steepest descent pathway is presented. This method is a Hessian based predictor-corrector algorithm that affords pathways comparable to our previous fourth order method at the cost of a second order approach. The proposed integrator is tested on an analytic surface, four moderately sized chemical reactions, and one larger organometallic system. (C) 2004 American Institute of Physics.