  We investigate the scalar potential of gauged N=4 supergravity with matter.
The extremum in the SU(1,1)/U(1) scalars is obtained for an arbitrary number of
matter multiplets. The constraints on the matter scalars are solved in terms of
an explicit parametrisation of an
  SO(6,6+n) element. For the case of six matter multiplets we discuss both
compact and noncompact gauge groups.
  In an example involving noncompact groups and four scalars we find a
potential with an absolute minimum and a positive cosmological constant.
