The decay asymmetries of the weak radiative Hyperon decays Ξ 0 → Λγ and Ξ 0 → Σ 0 γ have been measured with high precision using data of the NA48/1 experiment at CERN. From about 52 000 Ξ 0 → Λγ and 15 000 Ξ 0 → Σ 0 γ decays, we obtain for the decay asymmetries α Ξ 0 →Λγ = −0.704 ± 0.019 stat ± 0.064 syst and α Ξ 0 →Σ 0 γ = −0.729 ± 0.030 stat ± 0.076 syst , respectively. These results are in good agreement with previous experiments, but more precise.2