KEK-KEKB Collider. Measurement of the differential and total cross sections for PI0 PI0 production in two-photon collisions in the W range from 0.6 to 4.0 GeV and range of absolute(cos(theta*)) less than 0.8. The data sample comes from 95 pb-1 of E+ E- interactions around the Upsilon region (83 fb-1 at 10.58 GeV, 9 fb-1 at 10.52 GeV, 2.9 fb-1 at 10.36 GeV and 0.3 fb-1 at 10.30 GeV). The data at the different energies are combined introducing an error of less than 0.5% on the cross sections.. Numerical values supplied by S Uehara.