  We have introduced Faddeev-Niemi type variables for static SU(3) Yang-Mills
theory. The variables suggest that a non-linear sigma model whose sigma fields
take values in SU(3)/(U(1)xU(1)) and SU(3)/(SU(2)xU(1)) may be relevant to
infrared limit of the theory. Shabanov showed that the energy functional of the
non-linear sigma model is bounded from below by certain functional. However,
the Shabanov's functional is not homotopy invariant, and its value can be an
arbitrary real number -- therefore it is not a topological charge. Since the
third homotopy group of SU(3)/(U(1)xU(1)) is isomorphic to the group of integer
numbers, there is a non-trivial topological charge (given by the isomorphism).
We apply Novikov's procedure to obtain integral expression for this charge. The
resulting formula is analogous to the Whitehead's realization of the Hopf
invariant.
