As part of our on-going project on the homogeneous chemical characterization of multiple stellar populations in globular clusters ( GCs ) , we studied NGC 5634 , associated to the Sagittarius dwarf spheroidal galaxy , using high-resolution spectroscopy of red giant stars collected with FLAMES @ VLT . We present here the radial velocity distribution of the 45 observed stars , 43 of which are member , the detailed chemical abundance of 22 species for the seven stars observed with UVES-FLAMES , and the abundance of six elements for stars observed with GIRAFFE . On our homogeneous UVES metallicity scale we derived a low metallicity [ Fe/H ] = -1.867 \pm 0.019 \pm 0.065 dex ( \pm statistical \pm systematic error ) with \sigma = 0.050 dex ( 7 stars ) . We found the normal anti-correlations between light elements ( Na and O , Mg and Al ) , signature of multiple populations typical of massive and old GCs . We confirm the associations of NGC 5634 to the Sgr dSph , from which the cluster was lost a few Gyr ago , on the basis of its velocity and position and the abundance ratios of \alpha and neutron capture elements .