Cross sections for the photoproduction of neutral pions have been measured at the 1.1-GeV Frascati electron synchrotron for bombarding photon energies $k$ between 400 and 800 MeV and for ${\ensuremath{\pi}}^{0}$ c.m. angles of ${{\ensuremath{\theta}}_{\ensuremath{\pi}}}^{*}={90}^{\ensuremath{\circ}}, {120}^{\ensuremath{\circ}}, \mathrm{and} {135}^{\ensuremath{\circ}}$. The main feature of the experiment is good resolution in incident photon energy. The results are in good agreement with the existing theories in the energy range of 450 to 550 MeV. The cross sections exhibit a smooth behavior as a function of energy for $k=400\ensuremath{-}600$ MeV. No immediate evidence is found of a contribution of the ${P}_{11}$ resonance. An anomaly at the limit of statistical significance appears for $k\ensuremath{\simeq}700\ensuremath{-}740$ MeV, indicating a possible structure of the so-called second resonance. We attempt to interpret the observed anomaly as a reflection of the sharp opening of the $\ensuremath{\eta}$ production channel ($\ensuremath{\eta}$ cusp effect).