  We study the CMB constraint on non-Gaussianity in CDM isocurvature
perturbations. Non-Gaussian isocurvature perturbations can be produced in
various models at the very early stage of the Universe. Since the isocurvature
perturbations little affect the structure formation at late times, CMB is the
best probe of isocurvature non-Gaussianity at least in the near future. In this
paper, we focus on uncorrelated isocurvature perturbations and constrain their
non-Gaussianity. For this purpose, we employ several state-of-art techniques
for the analysis of CMB data and simulation. We use the WMAP 7 year data of
temperature anisotropy. When the adiabatic perturbations are assumed to be
Gaussian, we obtained a constraint on the isocurvature non-Gaussianity alpha^2
f_{NL}^{(ISO)}=40+-66 for the scale invariant isocurvature power spectrum,
where alpha is the ratio of the power spectrum of isocurvature perturbations to
that of the adiabatic ones. When we assume that the adiabatic perturbations can
also be non-Gaussian, we obtain f_{NL}=38+-24 and alpha^2
f_{NL}^{(ISO)}=-8+-72. We also discuss implications our results for the axion
CDM isocurvature model.
