  We prove that two formulas of the orbital magnetic susceptibility, namely,
Koshino-Ando's formula and G\'{o}mez-Santos and Stauber's formula, are
equivalent for the tight-binding models. The difference between these two
formulas can be written in a form containing the surface terms arising from the
momentum-space integration, and we show that the surface terms are exactly
vanishing although the primitive functions are seemingly non-periodic with
respect to the translation by the reciprocal lattice vector.
