  A novel method to calculate f_B on the lattice is introduced, based on the
study of the dependence of finite size effects upon the heavy quark mass of
flavoured mesons and on a non-perturbative recursive finite size technique. We
avoid the systematic errors related to extrapolations from the static limit or
to the tuning of the coefficients of effective Lagrangian and the results admit
an extrapolation to the continuum limit. We perform a first estimate at finite
lattice spacing, but close to the continuum limit, giving f_B = 170(11)(5)(22)
MeV. We also obtain f_{B_s} = 192(9)(5)(24) MeV. The first error is
statistical, the second is our estimate of the systematic error from the method
and the third the systematic error from the specific approximations adopted in
this first exploratory calculation. The method can be generalized to two--scale
problems in lattice QCD.
