Rare decays at CMS

The latest CMS results are presented on the search for the neutrino-less $\tau^{\pm}\to\mu^{\pm}\mu^{\pm}\mu^{\mp}$ decay, the first observation of the $\eta\to\mu^+\mu^-\mu^+\mu^-$ decay, the measurement of the $B^0_s\to\mu^+\mu^-$ branching fraction and effective lifetime, and the search for the $B^0\to\mu^+\mu^-$ decay. The results are based on data collected in proton-proton collisions at the centre of mass energy of 13 TeV.