A search for charged excited leptons decaying into a lepton and a photon has been performed using approximately 680 pb−1 of e+e− collision data collected by the OPAL detector at LEP at centre-of-mass energies between 183 and 209 GeV. No evidence for their existence was found. Upper limits on the product of the cross-section and the branching fraction are inferred. Using results from the search for singly produced excited leptons, upper limits on the ratio of the excited lepton coupling constant to the compositeness scale are calculated. From pair production searches, 95% confidence level lower limits on the masses of excited electrons, muons and taus are determined to be 103.2 GeV.