  The strong line broadening observed in electron spin resonance on
NaV$_2$O$_5$ is found to originate from an unusual type of the symmetric
anisotropic exchange interaction with simultaneous spin-orbit coupling on both
sites. The microscopically derived anisotropic exchange constant is almost two
orders of magnitude larger than the one obtained from conventional estimations.
Based on this result we systematically evaluate the anisotropy of the ESR
linewidth in terms of the symmetric anisotropic exchange, only, and we find
microscopic evidence for precursor effects of the charge ordering already below
150 K.
