  Phases of the spherical harmonic analysis of full-sky cosmic microwave
background (CMB) temperature data contain useful information complementary to
the ubiquitous angular power spectrum. In this letter we present a new method
of phase analysis on incomplete sky maps. It is based on Fourier phases of
equal-latitude pixel rings of the map, which are related to the mean angle of
the trigonometric moments from the full-sky phases. They have an advantage for
probing regions of interest without tapping polluted Galactic plane area, and
can localize non-Gaussian features and departure from statistical isotropy in
the CMB.
