  We investigate a statistical anisotropy on the Cosmic Microwave Background
(CMB) bispectrum, which can be generated from the primordial non-Gaussianity
induced by quantum fluctuations of a vector field. We find new configurations
in the multipole space of the CMB bispectrum given by $\ell_1 = \ell_2 + \ell_3
+ 2, |\ell_2 - \ell_3| - 2$ and their permutations, which violate the
rotational invariance, such as an off-diagonal configuration in the CMB power
spectrum. We also find that in a model presented by Yokoyama and Soda (2008),
the amplitude of the statistically anisotropic bispectrum in the above
configurations becomes as large as that in other configurations such as $\ell_1
= \ell_2 + \ell_3$. As a result, it might be possible to detect these
contributions in future experiments, which would give us novel information
about the physics of the early Universe.
