Hadronic events produced in e+e- collisions by the LEP collider and recorded by the OPAL detector were used to form distributions based on the number of reconstructed jets. The data were collected between 1995 and 2000 and correspond to energies of 91 GeV, 130-136 GeV and 161-209 GeV. The jet rates were determined using four different jet-finding algorithms (Cone, JADE, Durham and Cambridge). The differential two-jet rate and the average jet rate with the Durham and Cambridge algorithms were used to measure in the LEP energy range by fitting an expression in which calculations were matched to a NLLA prediction and fitted to the data. Combining the measurements at different centre-of-mass energies, the value of () was determined to beαS(MZ) = 0.1177 ± 0.0006 (stat.) ± 0.0012 (expt.) ± 0.0010 (had.) ± 0.0032 (theo.).