This paper describes a search for the Standard Model Higgs boson using data from e+e−e+e− collisions collected at center-of-mass energies of 161, 170 and 172 GeV by the OPAL detector at LEP. The data collected at these energies correspond to integrated luminosities of 10.0, 1.0 and 9.4 pb −1−1 , respectively. The search is sensitive to the main final states from the process in which the Higgs boson is produced in association with a fermion anti-fermion pair, namely four jets, two jets with missing energy, and two jets produced together with a pair of electron, muon or tau leptons. One candidate event is observed, in agreement with the Standard Model background expectation. In combination with previous OPAL searches at center-of-mass energies close to the Z 00 resonance and the revised previous OPAL searches at 161 GeV , we derive a lower limit of 69.4 GeV for the mass of the Standard Model Higgs boson at the 95% confidence level.