  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
$E=\pm\Delta$, $2\Delta$ being the Zeeman splitting. The conductivity is shown
to exhibit a box-like behavior with changing magnetic field: $\sigma_{xx}$ is
$\sim e^2/h$ at $|E_F|<\Delta$ and exponentially small otherwise. Two peaks of
$\sigma_{xx}$ arising as $T\to 0$ are found to be strongly asymmetric.

Condensed Matter