  It is shown that the account for the proton charge form factor in the Coulomb
corrections to the electron-proton scattering cross section noticeably
diminishes the difference between the value of the proton charge radius
$r_{\mathrm{E}}$, extracted from the $ep$ scattering data, and that following
from the muonic hydrogen data. For the electron energy much higher than the
electron mass but much smaller than $r_{\mathrm{E}}^{-1}\approx 230$~MeV, the
relative correction has the universal form $\delta
r_{\mathrm{E}}/r_{\mathrm{E}}=-\pi\alpha/2$, where $\alpha$ is the fine
structure constant.
