  The NLO QCD calculation for the photoproduction of the isolated photon with a
large pT at the HERA ep collider is presented. The single resolved photon
contribution and the QCD corrections of order alpha_s to the Born term are
consistently included. The NNLO contributions, the box and the double resolved
photon subprocesses, are sizeable and are taken into account in addition. The
importance of the isolation cut, as well as the influence of other experimental
cuts on pT and final photon rapidity distributions are discussed in detail. The
investigation of the renormalization scale dependence is performed in order to
estimate the size of missing higher order QCD corrections. Results are compared
with experimental data and with the prediction of a different NLO calculation.
