  Radiative corrections due to initial state radiation in electron-positron
annihilation are calculated within the QED structure function approach. Results
are shown in the next-to-leading logarithmic approximation up to $O(\alpha^4
L^3)$ order, where $L=\ln(s/m_e^2)$ is the large logarithm. Several mistakes in
previous calculations are corrected. The results are relevant for future
high-precision experiments at $e^+e^-$ colliders.
