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The hyperon weak radiative decay Ξ 0 → γ Σ 0 is measured using a sample of Ξ 0 from decays. The absolute branching fraction of Ξ 0 → γ Σ 0 is determined to be (3 . 66 ± 0 . 21 stat ± 0 . 10 syst ) × 10 − 3 , based on (10 . 087 ± 0 . 044) × 10 9 J/ψ events collected with the BESIII detector operating at the BEPCII collider. The decay asymmetry parameter is measured, with a complete angular analysis of the cascade decay chain, to be α γ = − 0 . 807 ± 0 . 095 stat ± 0 . 011 syst .