A search for the non-resonant decays B-s(0) -> mu(+) mu(-) mu(+)mu(-) and B-0 -> mu(+) mu(-) mu(+) mu(-) 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(B-s(0) -> mu(+) mu(-) mu(+)mu(-)) < 2.5 x 10(-9) B(B-0 -> mu(+) mu(-) mu(+) mu(-)) < 6.9 x 10(-10)