  The effects of the peculiar CP conserving phases in unparticle propagators
are explored. We find that the phases have a great impact on CP-violation. We
adopt the decays $B_{d}\to \pi^{+} \pi^{-}$ and $B_{d}\to \ell^{-}\ell^{+}$ as
the illustrators to demonstrate the influences of these phases on the direct CP
asymmetries. In particular, we emphasize that unparticle physics is the only
model suggested to date that could give the direct CP asymmetries in $B_d\to
\ell^{-} \ell^{+}$ as large as 15%. We also point out that the unparticle
phases could be probed in $B\to K^* \ell^{+} \ell^{-}$ decays by using T-odd
correlations.
