A direct search for pair produced magnetic monopoles in e+e- collisions at
LEP is reported. The analysis is based on 62.7 pb^{-1} of data collected
with the OPAL detector at an average centre-of-mass energy of sqrt(s) =
206.3 GeV. The monopole signal was assumed to be characterized by two
back-to-back tracks with an anomalously high ionization energy loss dE/dx
in the tracking chambers. No evidence for production of monopoles was
observed in the analysed data set. Upper limits were obtained on the
magnetic monopole pair-production cross-section in the mass range 
45 GeV/c^{2} < m_M <102 GeV/c^{2}.  The cross-section limit is derived at 
the 95 % confidence level and is valid for spin-1/2 magnetic monopoles.