  We study the possibility of an intermediate scale existing in supersymmetric
SO(10) grand unified theories: The intermediate scale is demanded to be around
10^{12} GeV so that neutrinos can obtain masses suitable for explaining the
experimental data on the deficit of solar neutrino with
Mikheev-Smirnov-Wolfenstein solution and the existence of hot dark matter. We
show that any Pati-Salam type intermediate symmetries are excluded by requiring
reasonable conditions and only $SU(2)_L\times SU(2)_R \times SU(3)_C\times
U(1)_{B-L}$ is likely to be realized as an intermediate symmetry.
