We report on measurements of the mass and lifetime of the Ξ(b)⁻ baryon using about 1800 Ξ(b)⁻ decays reconstructed in a proton-proton collision data set corresponding to an integrated luminosity of 3.0 fb⁻¹ collected by the LHCb experiment. The decays are reconstructed in the Ξ(b)⁻→Ξ(c)⁰π⁻, Ξ(c)⁰→pK⁻K⁻π⁺ channel and the mass and lifetime are measured using the Λ(b)⁰→Λ(c)⁺π⁻ mode as a reference. We measure M(Ξ(b)⁻)-M(Λ(b)⁰)=178.36±0.46±0.16 MeV/c², (τ(Ξ(b)⁻)/τ(Λ(b)⁰)=1.089±0.026±0.011, where the uncertainties are statistical and systematic, respectively. These results lead to a factor of 2 better precision on the Ξ(b)⁻ mass and lifetime compared to previous best measurements, and are consistent with theoretical expectations.