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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 = ∆. We further study the conductivity at the another extended state E = E 1 (E 1 > ∆). 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 ∆. We discuss also the case where the Zeeman energy ∆ becomes a random field.