  Gaussianity is the very base for derivation of the cosmological parameters
from the CMB angular power spectrum. Non-Gaussian signal, whether originated
from experimental error or primordial source, could mimic extra power in the
power spectrum, thereby leading to a wrong set of parameters. In this paper we
present a new Gaussianity analysis of the derived CMB singals. It is based on
the trigonometric moments of phases, which can be concluded with a ``mean
angle'', allowing us to see the global trend of non-Gaussianity of the signals.
These moments are also closely related to the Pearson's random walks. We apply
these analyses on the derived CMB maps and their different morphologies
manifest themselves through these functions. We also comment on rotational
invariance of the trigonometric moments of phases as a non-Gaussianity test.
