In this note, we show that the development for the calculation of nonadiabatic coupling vectors in the framework of TDDFT introduced by the authors in the series of recent publications [E. Tapavicza , Phys. Rev. Lett.98, 023001 (2007); I. Tavernelli , J. Chem. Phys.130, 124107 (2009)] is rigorous and fully equivalent to the one proposed by Sugino and co-workers [C. P. Hu , J. Chem. Phys.127, 064103 (2007)]. Specific applications of our formulation are also discussed.