The theory of the order-$\alpha$ radiative correction to the $\beta$ decay of baryons is briefly reviewed. An effective procedure for the calculation of the real-photonic part of the order-$\alpha$ correction is outlined. Numerical results are tabulated for the radiative corrections to the branching ratio, the electron-antineutrino correlation parameter, the electron-energy ($E_e$) spectrum, the final-baryon-energy ($E_f$) spectrum, and the electron-antineutrino angular-correlation ($E_e$) distribution, and to the ($E_f$, $E_f$) and the ($E_e$, $cos{\theta }_{e\nu }$) two-variable distributions in the cases of the decays ${\Sigma }^{-}\to \mathrm{ne}\overline{\nu }$, ${\Sigma }^{-}\to \Lambda e\overline{\nu }$, ${\Xi }^{-}\to \Lambda e\overline{\nu }$, and $\Lambda \to \mathrm{pe}\overline{\nu }$.

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