We propose a reaction path-based Hamiltonian in terms of the reaction coordinate, the curvature coordinate, the remaining 3N-8 transverse normal coordinates (whose directions are orthogonal to the path tangent and curvature vectors), and their conjugate momenta, for an N atomic reaction system. The 3N-8 transverse vibrational modes are independent of the motion along the reaction path, although they have coupling terms with the curvature direction in the harmonic approximation. A two-dimensional plane determined by the path tangent and curvature vectors is termed the "reaction plane." We introduce a function that estimates changes of the reaction plane along the reaction path, and analyze the reaction path based on this function for an abstraction reaction, CH3+H-2-->CH4+H. The scheme proposed here should be effective when a reaction path has a sharply curved region.