  The spherical Mexican Hat wavelet is introduced in this paper, with the aim
of testing the Gaussianity of the Cosmic Microwave Background temperature
fluctuations. Using the information given by the wavelet coefficients at
several scales, we have performed several statistical tests on the COBE-DMR
maps to search for evidence of non-Gaussianity. Skewness, kurtosis, scale-scale
correlations (for two and three scales) and Kolmogorov-Smirnov tests indicate
that the COBE-DMR data are consistent with a Gaussian distribution. We have
extended the analysis to compare temperature values provided by COBE-DMR data
with distributions (obtained from Gaussian simulations) at each pixel and at
each scale. The number of pixels with temperature values outside the 95% and
the 99% is consistent with that obtained from Gaussian simulations, at all
scales. Moreover, the extrema values for COBE-DMR data (maximum and minimum
temperatures in the map) are also consistent with those obtained from Gaussian
simulations.
