  We have investigated the odd-parity preference of the WMAP 7 year power
spectrum. Comparison with simulation shows the odd-parity preference of WMAP
data (2<= l <=22) is anomalous at 4-in-1000 level. We have investigated its
origins, and ruled out some of non-cosmological origins such as asymmetric
beams, noise and cut-sky effect. We also find primordial origin requires
|Re[\Phi(\mathbf k)]|\ll|Im[\Phi(\mathbf k)]| for k\lesssim 22/\eta_0, where
\eta_0 is the present conformal time. Multipoles associated with the odd-parity
preference happen to coincide with some of other CMB anomalies. Therefore,
there may exist a common origin, whether cosmological or not. Besides, we find
it likely that low quadrupole power is the part of this odd-parity preference
anomaly rather than an isolated one. The Planck surveyor, which possesses wide
frequency coverage and systematics distinct from the WMAP, may allow us to
resolve the mystery of the anomalous odd-parity preference.
