We have calculated the splitting functions governing the evolution of the unpolarized parton distributions of the photon at the next-to-next-to-leading order (NNLO) of massless perturbative QCD. The results, presented here mainly in terms of compact and accurate parametrizations, are consistent with our previous approximations based on the lowest six even-integer Mellin moments. Consequently the NNLO corrections are small in both the \overline {MS} and the {DIS}_\gamma factorization schemes at momentum fractions x \gsim 0.1.

PACS numbers: 12.38.Bx, 13.60.Hb, 13.66.Bc, 14.70.Bh