The complete census of globular clusters formerly belonging to the Sagittarius Dwarf Spheroidal (Sgr dSph) galaxy and now deposited into the Galactic halo is an important contribution to our comprehension of the evolution and disruption of this dwarf galaxy. We investigate in this study the possibility that the poorly known "old" globular AM 4 might be associated with the Sgr dSph galaxy, and at the same time provides more solid estimate of its basic parameters. New high-quality BVI photometry is presented, from which an improved color-magnitude diagram is constructed, and estimates of age and distance are then derived. The distance and Galactic position are finally investigated in detail. AM 4 is found to be a low-luminosity (M(V) = -1.82) cluster undergoing strong tidal stress by the Milky Way and on the verge to be dissolved. Besides, and at odds with previous suggestions, we provide evidences that AM 4 is indeed young, with an age around 9 Gyr (as Terzan 7), but somewhat more metal poor ([Fe/H= -0.97]). AM 4 is located at 33(-4)(+3) kpc from the Sun, in a direction and at distance not totally incompatible with the Sgr dSph stream. Although we significantly improved our knowledge of AM 4, further studies are encouraged to obtain radial velocity and metallicity to demonstrate more firmly (or deny) the association to Sgr.