  We determine the ratio FK/Fpi in QCD with Nf=2+1 flavors of sea quarks, based
on a series of lattice calculations with three different lattice spacings,
large volumes and a simulated pion mass reaching down to about 190 MeV. We
obtain FK/Fpi=1.192 +/- 0.007(stat) +/- 0.006(syst). This result is then used
to give an updated value of the CKM matrix element |Vus|. The unitarity
relation for the first row of this matrix is found to be well observed.
