Fermilab Tevatron. Measurement of the cross sections for direct photon pair production in PBAR P interactions at a centre-of-mass enegy of 1960 GeV. The data come from a sample of total integrated luminosity 4.2 fb-1 collected during the period from August 2006 to June 2009. Single differential cross sections as a function of diphoton mass, diphoton transverse momentum, the azimuthal angle between the photons and the cosine of the polar scattering angle in the frame with no net transverse momentum of the diphoton system are presented. Double differential cross sections are also measured as functions of the last three variables in three diphoton mass ranges.