  We report results from a search for the decay $B_s^0\rightarrow\eta\eta$
using 121.4 fb$^{-1}$ of data collected at the $\Upsilon(5S)$ resonance with
the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. We do not
observe any signal and set an upper limit on the branching fraction of
$14.3\times 10^{-5}$ at $90\%$ confidence level. This result represents a
significant improvement over the previous most stringent limit.
