A novel method of determining the mass of the W boson in the W+W- -> lnu lnu channel is presented and applied to 667pb^-1 of data recorded at the center-of- mass energies in the range 183-207 GeV with the OPAL detector at LEP. The Measured energies of charged leptons and the results of a new procedure based on an approximate kinematic reconstruction of the events are combined to give: Mw=80.41+-0.41+-0.13 GeV, when the first error is statistical and the second is systematic. The systematic error is dominated by the uncertainty on the lepton energy, which is calibrated using data, and the parameterization of the variables used in the fitting, which is obtained using Monte Carlo events. Both of these are limited by statistics.