The jet-jet profile, or detailed manner, in which transverse energy and mass are distributed around the jet-jet system resulting from the hadronic decay of a Z boson in the process Higgs to ZZ at a proton-proton collider energy of 40 TeV is carefully examined. Two observables are defined that can be used to help distinguish the lepton-lepton-jet-jet signal from Higgs decay from the "ordinary" QCD background arising from the large transverse momentum production of single Z bosons plus the associated jets. By making cuts on these observables, signal to background enhancement factors greater than 100 can be obtained.