We propose a new canonical procedure for investigating: non-Born-Oppenheimer dynamics. This procedure is based on Van Vleck's theory and expressed in the normal coordinates of one of the diabatically coupled electronic surfaces. Up to intermediate energies, the successive unitary transformations convert the smooth, non-resonant part of the energy shifts due to the diabatic coupling into anharmonicities and off-diagonal couplings inside each surface. As a result, in this energy range, the two transformed electronic surfaces remain fairly decoupled. We also show that, because of the reduced coupling range, the size of the matrix needed to calculate the exact energy levels:is substantially reduced, which is promising for future practical applications.