The study of reaction pathways is imperative to the investigation of potential energy surfaces. The intrinsic reaction coordinate is defined as the steepest descent path in mass weighted coordinates that connects the transition state to reactants and products. Various methods are available for following the intrinsic reaction coordinate. A potential energy surface may also be studied using classical trajectory calculations, and a dynamic reaction path method can be used to connect the transition state to reactants and products. We have modified a classical trajectory integration method such that the dynamic reaction pathway more closely resembles the intrinsic reaction coordinate. Specifically, a damped velocity Verlet algorithm incorporating a controlled time step is used. The efficiency of the present algorithm is on the same order as our earlier methods for relatively small systems and shows increasing efficiency as the large molecule limit is approached.