  We present a new, model-independent approach for measuring non-Gaussianity of
the Cosmic Microwave Background (CMB) anisotropy pattern. Our approach is based
on the empirical distribution function of the normalized spherical harmonic
expansion coefficients a_lm of a nearly full-sky CMB map, like the ones
expected from forthcoming satellite experiments. Using a set of
Kolmogorov-Smirnov type tests, we check for Gaussianity and independency of the
a_lm. We test the method on two non-Gaussian toy-models of the CMB, one
generated in spherical harmonic space and one in pixel (real) space. We also
provide some rigorous results, possibly of independent interest, on the exact
distribution of the spherical harmonic coefficients normalized by an estimated
angular power spectrum.
