A novel method of determining the mass of the W boson in the 
$\rm W^+W^-\rightarrow\ell\nu\ell^\prime\nu^\prime$  channel 
is presented and applied to
667\,pb$^{-1}$ of data recorded at 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:
\begin{center}{$\rm M_W = 80.41\pm 0.41\pm 0.13~GeV,$}
\end{center}
where 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.