We study AdS backgrounds of N=4 supergravity in four space-time dimensions
which preserve all sixteen supercharges. We show that the graviphotons have to
form a subgroup of the gauge group that consists of an electric and a magnetic
SO(3)_+ x SO(3)_-. Moreover, these N=4 AdS backgrounds are necessarily isolated
points in field space which have no moduli.Comment: 11 page