In this paper, it is proved that let G be a bipartite graph with bipartition (X, Y ) and with a perfect matching M , let G be an n-extendable graph, then G is minimally n-extendable if and only if, for any two vertices x ∈ X and y ∈ Y such that xy ∈ E(G), there are exactly n internally disjoint (x, y) M-alternating paths P1, P2, . . . , Pn such that Pi (1 i n) starts and ends with edges in E(G)...