Results of the search for the rare decay $B_s^0 \to \mu^+ \mu^-$ using data collected by the D0 detector at the Fermilab Tevatron collider are presented. This analysis covers the full Run II data set, corresponding to approximately 10.4~fb$^{-1}$ of integrated luminosity in $p\bar{p}$ collisions at a center of mass energy of 1.96 TeV. The analysis used new variables and a multivariate technique to improve the background reduction. After seeing fewer events than expected from background, a new Tevatron best observed limit was set on the branching fraction of the decay at $\cal{B}$($B_s^0 \to \mu^+ \mu^-$) $< 15 \times 10^{-9}$ ($12 \times 10^{-9}$) at the 95\% (90\%) C.L.