Search for rare decays

In these proceedings, the recent measurements of the $B_{s}^{0}\to\mu^{+}\mu^{-}$ decay branching fraction and its effective lifetime and the search for the $B^{0}\to\mu^{+}\mu^{-}$ decay using the data collected by the CMS experiment at LHC between the years 2011 and 2016 have been presented. Recently, a combined analysis of the decays $B_{s}^{0}\to\mu^{+}\mu^{-}$ and $B^{0}\to\mu^{+}\mu^{-}$ by ATLAS, CMS, and LHCb has been performed, which is also discussed in this paper. The third part of these proceeding includes the search for $\tau$ leptons decaying into three muons using the data collected by the CMS experiment in 2016.