  We compute the decay constants for the heavy--light pseudoscalar mesons in
the quenched approximation and continuum limit of lattice QCD. Within the
Schrodinger Functional framework, we make use of the step scaling method, which
has been previously introduced in order to deal with the two scale problem
represented by the coexistence of a light and a heavy quark. The continuum
extrapolation gives us a value $f_{B_s} = 192(6)(4)$ MeV for the $B_s$ meson
decay constant and $f_{D_s} = 240(5)(5)$ MeV for the $D_s$ meson.
