A search for a Higgs boson in the four-lepton decay channel H→ZZ, with each Z boson decaying to an electron or muon pair, is reported. The search covers Higgs boson mass hypotheses in the range of 110<mH<600  GeV. The analysis uses data corresponding to an integrated luminosity of 4.7  fb−1 recorded by the CMS detector in pp collisions at √s=7  TeV from the LHC. Seventy-two events are observed with four-lepton invariant mass m4ℓ>100  GeV (with 13 below 160 GeV), while 67.1±6.0 (9.5±1.3) events are expected from background. The four-lepton mass distribution is consistent with the expectation of standard model background production of ZZ pairs. Upper limits at 95% confidence level exclude the standard model Higgs boson in the ranges of 134–158 GeV, 180–305 GeV, and 340–465 GeV. Small excesses of events are observed around masses of 119, 126, and 320 GeV, making the observed limits weaker than expected in the absence of a signal.