A reaction path Hamiltonian is formulated in terms of a Newton reference path. The defining differential equation for the latter is solved by quadratically expanding the original equation, which in turn leads to an improved formulation of the reaction path Hamiltonian. This new reference path is found to deal properly with bifurcation points, a difficulty not solved by intrinsic reaction coordinate-following algorithms. The Newton path is found, in addition, to be reliable as for the description of chemical rearrangement processes, as it is illustrated with the application to the HCN<->CHN isomerization as well as the 1,2 hydrogen migration between ethyne oxide and the corresponding carbene.