First measurements of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:math>decays into<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>Σ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mover accent="true"><mml:mi>Σ</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mo>−</mml:mo></mml:msup></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>Ξ</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mover accent="true"><mml:mi>Ξ</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mn>0</mml:mn></mml:msup></mml:math>

Based on $58\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $J/\ensuremath{\psi}$ events collected with the BESII detector at the Beijing Electron-Positron Collider, the baryon pair processes $J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{+}{\overline{\ensuremath{\Sigma}}}^{\ensuremath{-}}$ and $J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\Xi}}^{0}{\overline{\ensuremath{\Xi}}}^{0}$ are observed for the first time. The branching fractions are measured to be $\mathcal{B}(J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{+}{\overline{\ensuremath{\Sigma}}}^{\ensuremath{-}})=(1.50\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.22)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $\mathcal{B}(J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\Xi}}^{0}{\overline{\ensuremath{\Xi}}}^{0})=(1.20\ifmmode\pm\else\textpm\fi{}0.12\ifmmode\pm\else\textpm\fi{}0.21)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, where the first errors are statistical and the second ones are systematic.