The decay width and mass of the D_(s1)(2536)^+ meson are measured via the decay channel D_(s1) + →D^(*+)K_(S)^0 using 385 fb^(-1) of data recorded with the BABAR detector in the vicinity of the Υ(4S) resonance at the PEP-II asymmetric-energy electron-positron collider. The result for the decay width is Γ(D_(s1)^+) = 0.92 ± 0.03(stat.) ± 0.04(syst.) MeV. For the mass, a value of m(D_(s1)^+) = 2535.08±0.01(stat.) ± 0.15(syst.) MeV/c^2 is obtained. The mass difference between the D_(s1)^+ and the D^(*+) is measured to be m(D_(s1)^+) - m(D^(*+)) = 524.83 ± 0.01(stat.) ± 0.04(syst.) MeV/c^2, representing a significant improvement compared to the current world average. The unnatural spin-parity assignment for the D_(s1)^+ meson is confirmed
