Results of the search for $sim (10^{16} - 10^{17.5})$ eV primary cosmic-ray photons with the data of the Moscow State University (MSU) Extensive Air Shower (EAS) array are reported. The full-scale reanalysis of the data with modern simulations of the installation does not confirm previous indications of the excess of gamma-ray candidate events. Upper limits on the corresponding gamma-ray flux are presented. The limits are the most stringent published ones at energies $sim 10^{17}$ eV.