  We consider the Hall conductivity of two-dimensional non-interacting Bloch
electrons when the magnetic flux per unit cell is a rational number $p/q$ where
$p$ and $q$ are mutually coprime. We present a counter-example for the naive
expectation that the Hall conductivity carried by a band is given by treating
gap minima as Dirac fermions. Instead of the above expectation, we show that
the {\em change\/} of the Hall conductivity at a gap-closing phenomenon is
given by the Dirac fermion argument. Comparing with the Diophantine equation,
our result implies that a band-gap closes at $q$ points simultaneously.
Furthermore, we show that the dispersion relation is $q$-fold degenerate in the
magnetic Brillouin zone.
