  We present a precise determination of the leptonic decay constant F_D(s) of
the D(s)-meson in quenched lattice QCD. This work is particularly focused on
the analysis and discussion of all sources of systematic errors. We simulate
directly at the physical quark masses for five different lattice spacings
between 0.1fm and 0.03fm using O(a)-improvement. The finest lattice is still
work in progress. After taking the continuum limit and setting the scale with
the Kaon decay constant F_K=160MeV we arrive at a value of F_D(s)=252(9)MeV.
Setting the scale with the nucleon mass instead leads to a decrease of about
20MeV of F_D(s).
