This Letter describes a direct search for pair produced magnetic monopoles in
e+e− collisions. The analysis is based on 62.7 pb
−1 of data collected with the OPAL detector at an average centre-of-mass energy of
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. The monopole signal was assumed to be characterized by two back-to-back particles with an anomalously high ionization energy loss
dE/dx in the tracking chambers. No evidence for production of monopoles was observed. Upper limits were obtained on the magnetic monopole pair-production cross-section (
σ) in the mass range
45 GeV/c2<mM<102 GeV/c2. The average limit is
σ<0.05 pb and is essentially independent of the magnetic monopole mass. The cross-section limit is derived at the 95%confidence level and is valid for spin-1/2 magnetic monopoles.