  We report the results of the first search for the decay $B_s^0 \rightarrow
\eta^\prime \eta$ using $121.4~\textrm{fb}^{-1}$ of data collected at the
$\Upsilon(5S)$ resonance with the Belle detector at the KEKB asymmetric-energy
$e^+e^-$ collider. We observe no significant signal and set a 90\%
confidence-level upper limit of %$7.1 \times 10^{-5}$ $6.5 \times 10^{-5}$ on
the branching fraction of this decay.
