  An extended formula for orbital susceptibility including corrections of the
Peierls phase is introduced. By using the new developed formula, the orbital
susceptibility of benzene is estimated analytically on the basis of the $\pi$
electron approximation. As a result, it is found that the orbital
susceptibility is 1.2 times larger than that estimated only from the Peierls
phase. The Coulomb interaction dependence of the orbital susceptibility of
benzene is also discussed by using exact diagonalization. It is found that the
absolute value of the orbital susceptibility decreases as the Coulomb
interaction increases, while the ratio of the orbital susceptibility with and
without the corrections of the Peierls phase increases. Finally, we discuss the
orbital susceptibility of a single-band tight-binding model on a square
lattice. We clarify that the correction of the Peierls phase is comparable to
the Landau--Peierls orbital susceptibility and that it corresponds to the Fermi
sea term.
