The first observation of the rare $\eta \to \mu^+\mu^-\mu^+\mu^-$ double-Dalitz decay is presented. The analysis is based on data collected by the CMS experiment at the CERN LHC operating at the centre-of-mass energy of $\sqrt{s}=13\, {\rm TeV}$. The data sample was collected with high-rate muon triggers for an integrated luminosity of $101\, {\rm fb^{-1}}$.
The branching fraction of the $\eta \to 4\mu$ decay is measured relative to the $\eta \to 2\mu$ decay yielding a value of $\mathcal{B}(\eta \to \mu^+\mu^-\mu^+\mu^-)=[5.0\pm0.8({\rm stat}) \pm0.7({\rm syst})\pm0.7({\mathcal{B}_{2\mu}})]\times 10^{-9}$, in agreement with the Standard Model theoretical predictions.