  The quantum Hall system in the lowest Landau level with Zeeman term is
studied by a two-state model, which has a chiral invariance. Using a
diagrammatic analysis, we examine this two-state model with random impurity
scattering, and find the exact value of the conductivity at the Zeeman energy
$E = \Delta$. We further study the conductivity at the another extended state
$E = E_1$ ($ E_1 > \Delta$). We find that the values of the conductivities at
$E = 0$ and $E = E_1$ do not depend upon the value of the Zeeman energy
$\Delta$. We discuss also the case where the Zeeman energy $\Delta$ becomes a
random field.
