  The chiral model for self-dual gravity given by Husain in the context of the
chiral equations approach is discussed. A Lie algebra corresponding to a finite
dimensional subgroup of the group of symplectic diffeomorphisms is found, and
then use for expanding the Lie algebra valued connections associated with the
chiral model. The self-dual metric can be explicitly given in terms of harmonic
maps and in terms of a basis of this subalgebra.
