  The anomaly against the Gaussianity in the WMAP data was alleged to be due to
insufficient handling of beam asymmetries. In this paper we investigate this
issue and develop a method to estimate the shape of the inflight effective
beam, particularly the asymmetry and azimuthal orientation. We divide the whole
map into square patches and exploit the information in the Fourier space. For
patches containing bright extra-galactic point sources, we can directly
estimate their shapes, from which the inflight effective beam manifests itself.
For those without, we estimate the pattern via perturbing the phases and
directly from the Fourier amplitudes. We show that the inflight effective beam
convolving the signal is indeed non-symmetric for most part of the sky, and
it's not randomly oriented. Around the ecliptic poles, however, the asymmetry
is smaller due to the averaging effect from different orientations of the beam
from the scan strategy. The effective beam with significant asymmetry is
combing with almost parallel fashion along the lines of Ecliptic longitude. In
the foreground-cleaned ILC map, however, the systematics caused by beam effect
is significantly lessened.
