A new method to derive an upper limit on photon primaries from small data sets of air showers is developed which accounts for shower properties varying with the primary energy and arrival direction. Applying this method to the highest-energy showers recorded by the AGASA experiment, an upper limit on the photon fraction of 51% (67%) at a confidence level of 90% (95%) for primary energies above 1.25 x 10(20) eV is set. This new limit on the photon fraction above the Greisen-Zatsepin-Kuzmin cutoff energy constrains the -burst model of the origin of highest-energy cosmic rays.