A search for the non-resonant decays Bs0 → μ+μ−μ+μ− and B0 → μ+μ−μ+μ− is presented. The measurement is performed using the full Run 1 data set collected in proton-proton collisions by the LHCb experiment at the LHC. The data correspond to integrated luminosities of 1 and 2 fb−1 collected at centre-of-mass energies of 7 and 8 TeV, respectively. No signal is observed and upper limits on the branching fractions of the non-resonant decays at 95% confidence level are determined to be
B(B0s→μ+μ−μ+μ−)<2.5×10−9,
B(Bs0→μ+μ−μ+μ−)<2.5×10−9,
B(B0→μ+μ−μ+μ−)<6.9×10−10.