In this Letter the Curl condition related to the nonadiabatic coupling terms, proved to be fulfilled by Born-Oppenheimer electronic eigenfunctions [Chem. Phys. Lett. 35 (1975) 112], is extended to include the points of singularity as recently discussed [Chem. Phys. 259 (2000) 123, Appendix B]. The study, related at this stage to a two-state system, is expected to add insight as to the origin of the non-adiabatic coupling terms.