  A bond-operator mean-field theory in the SU(3) bosons representation is
developed to describe the antiferro-nematic phase of the spin-1
bilinear-biquadratic model. The calculated static structure factors reveal
delicately that the antiferro-nematic state may exhibit both the ferro- and
antiferro-quadruple long-range orders, which is reminiscent of the ferrimagnets
or the canted antiferromagnets. This result may influence the spin wave theory
concerned with this phase. Possible relevance of this unconventional state to
the quasi-two-dimensional triangular material NiGa2S4 is addressed.
