  We investigate the magneto-transport properties of electrons on a square
lattice under a magnetic field with the alternate flux strength
$\phi\pm\Delta\phi$ in neighboring plaquettes. A new peculiar behavior of the
Hall conductance has been found and is robust against weak disorder: if
$\phi={p\over{2N}}\times{2\pi}$ ($p$ and $2N$ are coprime integers) is fixed,
the Chern numbers of Landau subbands will be redistributed between neighboring
pairs and hence the total quantized Hall conductance exhibits a direct
transition by $\pm{N}e^2/h$ at critical fillings when $\Delta\phi$ is increased
from 0 up to a critical value $\Delta\phi_c$. This effect can be an
experimental probe of the staggered-flux phase.
