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 root S = 206.3 GeV. 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 (sigma) in the mass range 45 GeV/c(2) < m(M) < 102 GeV/c(2). The average limit is sigma < 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. (C) 2008 Published by Elsevier B.V.