  We obtain an explicit parametrization of stationary discs glued to some Levi
non-degenerate hypersurfaces. These discs form a family which is invariant
under the action of biholomorphisms. We use this parametrization to construct a
local circular representation of these hypersurfaces. As a corollary, we get
the uniqueness of biholomorphisms with given 1-jet at some convenient point.
