The decay width and mass of the Ds1(2536)+ meson are measured via the decay channel Ds1+→D*+KS0 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(Ds1+)=0.92±0.03(stat.)±0.04(syst.) MeV. For the mass, a value of m(Ds1+)=2535.08±0.01(stat.)±0.15(syst.) MeV/c2 is obtained. The mass difference between the Ds1+ and the D*+ is measured to be m(Ds1+)-m(D*+)=524.83±0.01(stat.)±0.04(syst.) MeV/c2, representing a significant improvement compared to the current world average. The unnatural spin-parity assignment for the Ds1+ meson is confirmed.