Anomalous couplings of the Higgs boson are searched for through the processes e+e−→Hγ, e+e−→e+e−H and e+e−→HZ. The mass range 70 GeV<190 GeV is explored using 602 pb−1 of integrated luminosity collected with the L3 detector at LEP at centre-of-mass energies √s=189–209 GeV. The Higgs decay channels , H→γγ, H→Zγ and are considered and no evidence is found for anomalous Higgs production or decay. Limits on the anomalous couplings d, dB, Δg1Z, Δκγ and ξ2 are derived as well as limits on the H→γγ and H→Zγ decay rates.