  We summarize a computation of the leptonic decay constant f_D_s of the
D_s-meson in quenched QCD on the lattice. We perform a direct simulation at the
masses of the strange and the charm quarks at four different lattice spacings
from approximately 0.1 fm to 0.05 fm. Fully non perturbative O(a)-improvement
is employed. After taking the continuum limit we arrive at a value of
f_D_s=252(9) MeV, when setting the scale with the Kaon decay constant f_K=160
MeV. Setting the scale with the nucleon mass instead leads to a decrease of
about 20 MeV of f_D_s.
