We present data on proton-proton collisions, obtained at the CERN Intersecting Storage Rings, in which two roughly back-to-back π0's of high transverse momentum (pT) were produced. The angular distribution of the dipion axis relative to the collision axis is found to be independent of both the effective mass m of the dipion system and the centre-of-mass energy √s of the proton-proton collision. The cross-sections dσ dm at the values of √s satisfy a scaling law of the form dσ dm = G(x) mn, where x = m(π0, π0)//trs and n = 6.5 ± 0.5. We show from our data that the leading π0 carries most of the momentum of the scattered parton. Given this fact, the axis of the dipion system follows closely the direction of the scattered constituents, and we exploit this to determine the angular dependence of the hard-scattering subprocess. We also compare our data with the lowest order QCD predictions using structure functions as determined in deep-inelastic scattering and fragmentation functions from electron-positron annihilation.