The energy spectrum of cosmic rays above 2.5 × 10¹⁸ eV, derived from 20,000 events recorded at the Pierre Auger Observatory, is described. The spectral index γ of the particle flux, J ∝ E-γ, at energies between 4 × 10¹⁸ eV and 4 × 10¹⁹ eV is 2.69 ± 0.02(stat) ± 0.06(syst), steepening to 4.2 ± 0.4(stat) ± 0.06(syst) at higher energies. The hypothesis of a single power law is rejected with a significance greater than 6 standard deviations. The data are consistent with the prediction by Greisen and by Zatsepin and Kuz'min.