  A search for the decay $K^0_{\scriptscriptstyle S}\to\mu^+\mu^-$ is
performed, based on a data sample of proton-proton collisions corresponding to
an integrated luminosity of 3 fb$^{-1}$, collected by the LHCb experiment at
centre-of-mass energies of 7 and 8 TeV. The observed yield is consistent with
the background-only hypothesis, yielding a limit on the branching fraction of
${\cal B}(K^0_{\scriptscriptstyle S}\to\mu^+\mu^-) < 0.8~(1.0) \times 10^{-9}$
at $90\%~(95\%)$ confidence level. This result improves the previous upper
limit on the branching fraction by an order of magnitude.
