The quantum Hall regime in a smooth random potential is considered when two disorder-broadened Zeeman levels overlap strongly. Spin-orbit coupling is found to cause a drastic change in the percolation network which leads to a strong enhancement of the dissipative conductivity at finite temperature, provided the Fermi level E_F lies between the energies of two delocalized states E=±Δ, 2Δ being the Zeeman splitting. The conductivity is shown to exhibit a box-like behavior with changing magnetic

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... eld: σ_xx is ∼ e^2/h at |E_F|<Δ and exponentially small otherwise. Two peaks of σ_xx arising as T→ 0 are found to be strongly asymmetric.