  Using special linear combinations of finite energy sum rules which minimize
the contribution of the unknown continuum spectral function, we compute the
decay constants of the pseudoscalar mesons B and B_s. In the computation, we
employ the recent three loop calculation of the pseudoscalar two-point function
expanded in powers of the running bottom quark mass. The sum rules show
remarkable stability over a wide range of the upper limit of the finite energy
integration. We obtain the following results for the pseudoscalar decay
constants: f_B=178 \pm 14 MeV and f_{B_s}=200 \pm 14 MeV. The results are
somewhat lower than recent predictions based on Borel transform, lattice
computations or HQET. Our sum rule approach of exploiting QCD quark hadron
duality differs significantly from the usual ones, and we believe that the
errors due to theoretical uncertainties are smaller.
