  It is possible that the primordial non-Gaussianity is dominated by the higher
order terms, such as that set by $g_{NL}$, not $f_{NL}$. In this paper we
derive the spectral index and running of $g_{NL}$ from a single isocurvature
scalar field. The scale dependences of non-Gaussianity parameters are
detectable if the mass of isocurvature field is not too small compared to the
Hubble parameter during inflation. In addition, we also apply our results to
investigate the curvaton model with near quadratic potential in detail.
