The branching ratio of the η meson decay to four muons has not yet been experimentally confirmed. While this decay is predicted theoretically, the comparatively large mass of the muons suggests that the branching ratio is extremely low, on the scale of 10^-9. As the Compact Muon Solenoid (CMS) experiment has collected a vast quantity of data concerning particle decays, it is possible for rare decays such as this one to still produce discernible peaks. After selecting an appropriate subset of the total data that could possibly contain this decay, a peak is indeed found near 0.55 GeV, the η mass. Performing a Gaussian fit to this peak against a polynomial background suggests that the peak is not the result of statistical fluctuations in the background. To calculate the branching ratio, the number of signal events within the peak is then extracted from the fit. Other necessary quantities such as the acceptance and the production cross-section are found using Monte Carlo simulations. The obtained branching ratio is (4.1 ± 1.1) ✕ 10^-9. This value is consistent with both theoretical values and the current experimental upper limit.