We define and prove uniqueness of a natural homomorphism (called the Orchard morphism)from some groups associated naturally to a finite set $E$ to thegroup ${\mathcal E}(E)$ of two-partitions of $E$ representing equivalence relations having at most two classes on $E$.As an application, given a finite generic configuration ${\mathcal C}\subset{\mathbf R}^d$, we exhibit a natural partition of ${\mathcal C}$ in two sets.