Using data collected at centre-of-mass energies from 183 to 207 GeV with the OPAL detector at LEP, which amount to an integrated luminosity of 667.4 pb^-1, the mass of the W boson is measured in the fully leptonic channel, WW->lvlv. The W mass is determined with an unbinned fit based on a parametrization of two distributions: the first is the pseudomass which is obtained from an approximative reconstruction of the events and the second is the directly measured energies of the charged leptons.