Let M be an irreducible complex space. Classically, an analytic equivalence relation on M is defined by its graph which is an analytic subset \(\mathcal {R} \subset M \times M\) and M admits a holomorphic quotient with respect to R if the quotient space \(M/\mathcal {R}\) , endowed with the sheaf of invariant holomorphic functions, is a complex space. In his fundamental paper, Henri Cartan studies the case of a proper analytic equivalence relation \(\mathcal {R}\) on M, which is the case where the first canonical projection \(p_1\colon \mathcal {R} \rightarrow M\) is a proper holomorphic map. In his article he gives a necessary and sufficient condition for the existence of a holomorphic quotient of M with respect to \(\mathcal {R}\) . But this condition is not always fulfilled, even in the case where M is compact.