  We investigate the effect of unparticles in the pure annihilation type decays
$B^- \to D_s^-\phi $ and $ D_s^- K^{*0}$. Since these decays have only
annihilation contributions their branching ratios are expected to be very small
in the standard model and the direct CP asymmetry parameters to be zero. We
find that due to the unparticle effect these branching ratios can be
significantly enhanced from their standard model values. Furthermore, sizable
nonzero direct CP violation could also be possible in these channels due to the
presence of intrinsic CP conserving phase in the unparticle propagator.
