  We construct the so far unknown Lagrangian of D=6, N=2 F(4) Supergravity
coupled to an arbitrary number of vector multiplets whose scalars span the
coset manifold SO(4,n)/{SO(4) x SO(n)}.
  This is done first in the ungauged case and then extended to the compact
gauging of SU(2) x G, where SU(2) is the R-symmetry diagonal subgroup of
SU(2)_L x SU(2)_R = SO(4) and G is a compact subgroup of SO(n), n being the
number of vector multiplets, and such that dim G = n.
  The knowledge of the Lagrangian allows in principle to refine the AdS_6/CFT_5
correspondence already discussed, as far as supersymmetric multiplets are
concerned, in a previous related paper. With respect to the latter we also give
a more exaustive treatment of the construction of the theory at the level of
superspace Bianchi identities and in particular of the scalar potential.
