A search for the decay B 0 s → K * 0 µ + µ − is presented using data sets corresponding to 1.0, 2.0 and 1.6 fb −1 of integrated luminosity collected during pp collisions with the LHCb experiment at centre-of-mass energies of 7, 8 and 13 TeV, respectively. An excess is found over the background-only hypothesis with a significance of 3.4 standard deviations. The branching fraction of the B 0 s → K * 0 µ + µ − decay is determined to be The observation of the rare b → d + − FCNC decays B + → π + µ + µ − and Λ 0 b → pπ − µ + µ − has been previously reported by the LHCb collaboration in refs.[9] and [10], respectively. Evidence for the decay B 0 → π + π − µ + µ − has also been established in ref. [11]. The decay B 0 s → K * 0 µ + µ − has not yet been observed. The measured ratio of the B + → π + µ + µ − and B + → K + µ + µ − branching fractions has also been used to determine the ratio of CKM elements |V td /V ts | [12], exploiting correlations between the B → K and B → π form-factors in lattice computations. A similar approach could, in the future, be applied to the ratio of the B 0 s → K * 0 µ + µ − and B 0 → K * 0 µ + µ − decay rates [13]. The decay B 0 → K * 0 µ + µ − , which involves a b → s + − transition, has been studied extensively by BaBar, Belle, CDF and by the LHC experiments [14][15][16][17][18][19]. The rate of the -1 -