It has been recently shown by us, on the basis of crystal structure database that the flexibility of B-DNA double helices depends significantly on their base sequence. Our model building studies further indicated that the existence of bifurcated cross-strand hydrogen bonds between successive base pairs is possibly the main factor behind the sequence directed DNA flexibility. These cross-strand hydrogen bonds are, of course, weaker than the usual Watson-Crick hydrogen bonds and their bond geometry is characterized by relatively larger bond lengths and smaller bond angles. We have tried to improve our model structures by incorporating non-planarity of the amino groups in DNA bases due to the presence of lone pair electrons at the nitrogen atoms. Energy minimization studies have been carried out by using different quantum chemical methods, whereby it is found that in all cases of N - H....O type cross-strand hydrogen bonds, the bond geometry improves significantly. In the cases of N - H....N type hydrogen bonds, however, no such consistent improvements can be noticed. Perhaps the true picture would emerge only if all the other interactions present in the DNA macromolecule could be appropriately taken into account.