  We perform the non-linear realisation or the coset formulation of the pure
N=4, D=5 supergravity. We derive the Lie superalgebra which parameterizes a
coset map whose induced Cartan-Maurer form produces the bosonic field equations
of the pure N=4, D=5 supergravity by canonically satisfying the Cartan-Maurer
equation. We also obtain the first-order field equations of the theory as a
twisted self-duality condition for the Cartan-Maurer form within the
geometrical framework of the coset construction.
