We present formulae for the joint angular distributions for $J/\psi$ or $\psi (2S)$ decays into $\Lambda \overline{\Lambda }$, ${\Sigma }^0{\overline{\Sigma }}^0$, ${\Xi }^{-}{\overline{\Xi }}^{+}$, and ${\Omega }^{-}{\overline{\Omega }}^{+}$, which allows the determination of the antihyperon decay parameters using helicity amplitude information. The prospects of measuring the antihyperon decay parameters in these decays are discussed. The estimation of the measurement sensitivity shows that $J/\psi$ decays into $\Lambda \overline{\Lambda }$ and ${\Xi }^{-}{\overline{\Xi }}^{+}$ can be hopefully used to measure the $\overline{\Lambda }$ and ${\overline{\Xi }}^{+}$ decay parameters.

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