A sample of 3120 K-+/- -> pi(+/-)mu(+)mu(-) decay candidates with (3.3 +/- 0.7)% background contamination has been collected by the NA48/2 experiment at the CERN SPS, allowing a detailed study of the decay properties. The branching ratio was measured to be BR = (9.62 +/- 0.25) x 10(-8). The form factor W(z), where z = (M-mu mu/M-K)(2), was parameterized according to several models. In particular, the slope of the linear form factor W(z) = W-0(1 + delta z) was measured to be delta = 3.11 +/- 0.57. Upper limits of 2.9 x 10(-2) and 2.3 x 10(-2) on possible charge asymmetry and forward-backward asymmetry were established at 90% CL. An upper limit BR(K-+/- -> pi(-/+)mu(+/-)mu(+/-)) < 1.1 x 10(-9) was established at 90% CL for the rate of the lepton number violating decay. (C) 2011 Elsevier B.V. All rights reserved.