In this paper the following theorem is proved. Let G be a finite Abelian group of order n. Then, n+D (G)-1 is the least integer m with the property that for any sequence of m elements a1,..., am in G, 0 can be written in the form 0=a1+...+ain with 1≤i1<...<in≤m, where D (G) is the Davenport's constant on G, i.e., the least integer d with the property that for any sequence of d elements in G, there exists a nonempty subsequence that the sum of whose elements is 0.