LetXandYbe complex analytic manifolds of the same complex dimension, letpbe a point inT*X\{0} and letqbe a point inT*Y\{0}. Let ϵ (p) (resp. ϵ (q)) denote the graded ring of germs of micro-differential operators atp(resp.q). Supply ϵ (p) and ϵ (q) with a suitable and natural convergence structure. Let X: ϵ (p) ϵ → (q) be a continuous degree preserving ring isomorphism. We show that there exists a vector field ∂ tangent toXin a neighbourhood of л(q), a symplectic map ф defined on a conic open neighbourhood ofqto a similar neighbourhood ofpsuch thatfor an appropriate constantzand a suitable invertible elementA. in ϵ (q) of degree 0. Uniqueness of this result is discussed and a global version is also given. Here < ∂, ξ > denotes the duality betweenT(Y) andT*(Y). of do,(X) = 1, then this representation is canonical.