  We provide a new value for the ratio $R={\Gamma(\pi^0\to
e^+e^-\gamma(\gamma))}/{\Gamma(\pi^0\to\gamma\gamma)}=11.978(6)\times10^{-3}$,
which is by two orders of magnitude more precise than the current Particle Data
Group average. It is obtained using the complete set of the
next-to-leading-order radiative corrections in the QED sector, and incorporates
up-to-date values of the $\pi^0$-transition-form-factor slope. The ratio $R$
translates into the branching ratios of the two main $\pi^0$ decay modes:
$\mathcal{B}(\pi^0\to\gamma\gamma)=98.8131(6)\,\%$ and $\mathcal{B}(\pi^0\to
e^+e^-\gamma(\gamma))=1.1836(6)\,\%$.
