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1 IntroductionrnLet A be a collection of n pairwise disjoint simple closed curves on an orientable closed surface F of genus n ≥ 2. We say that A is a complete system of F if the surface obtained by cutting F along A is a 2n-punctured sphere. Let A1,A2 be two non-empty subsets of A. We say that (A1, A2) is a partition of A if A1 ∩ A2 =φ and A1 ∪A2 = A. Let (A1, A2)be a partition of A on F, and C a simple closed curve on F. We say that C is separating with respect to (A1, A2) if it is disjoint from A and it cuts F into two pieces F1, F2 with A1 (∈) F1, A2(∈) F2.