  We present the first (V,V-I) Color -- Magnitude Diagram (CMD) for the poorly
studied globular cluster NGC 5634. The CMD shows a steep Red Giant Branch (RGB)
and a predominantly blue Horizontal Branch (HB): both these characteristics
suggest a low metal content for this cluster. From the position of the RGB in
the CMD we estimate [Fe/H] = -1.94 +/- 0.10 and E(B-V)=0.06 +/- 0.01. The CMD
presented here reaches V\simeq 23, allowing us to obtain the first measure of
the Main Sequence Turn-Off (TO) V_{TO}= 21.22 +/- 0.15 for this cluster. By
combining this figure with the apparent luminosity of the Zero Age HB (ZAHB),
V_{ZAHB}=17.90 +/- 0.10 we obtain Delta V^{HB}_{TO}=3.32 +/- 0.16, a value
which is fully compatible with that derived for the bulk of Galactic globulars.
We also derive a true distance modulus of (m-M)_0 = 17.17 +/- 0.12
corresponding to a distance of ~ 27.2 kpc. Most interestingly, the cluster is
shown to have position and radial velocity fully compatible with the orbit of
the Sgr dwarf spheroidal (dSph) galaxy. The similarity between the stellar
populations of the cluster and the Sgr globular Ter 8 and the metal poor
population of the Sgr dSph, also suggest that NGC 5634 was a former member of
this disrupting galaxy, torn off by the Galactic tidal field and now lost in
the Sgr Stream.
