  We study the statistical properties of the 1st year WMAP data on different
scales using the spherical mexican hat wavelet transform. Consistent with the
results of Vielva et al. (2003) we find a deviation from Gaussianity in the
form of kurtosis of wavelet coefficients on $3-4^\circ$ scales in the southern
Galactic hemisphere. This paper extends the work of Vielva et al. as follows.
We find that the non-Gaussian signal shows up more strongly in the form of a
larger than expected number of cold pixels and also in the form of scale-scale
correlations amongst wavelet coefficients. We establish the robustness of the
non-Gaussian signal under more wide-ranging assumptions regarding the Galactic
mask applied to the data and the noise statistics. This signal is unlikely to
be due to the usual quadratic term parametrized by the non-linearity parameter
$f_{NL}$. We use the skewness of the spherical mexican hat wavelet coefficients
to constrain $f_{NL}$ with the 1st year WMAP data. Our results constrain
$f_{NL}$ to be $50\pm 80$ at 68% confidence, and less than 280 at 99%
confidence.
