Let G be a connected hypergraph with even uniformity,which contains cut vertices.Then G is the coalescence of two nontrivial connected sub-hypergraphs (called branches) at a cut vertex.Let (A)(G) be the adjacency tensor of G.The least H-eigenvalue of (A)(G) refers to the least real eigenvalue of (A)(G) associated with a real eigenvector.In this paper,we obtain a perturbation result on the least H-eigenvalue of (A)(G) when a branch of G attached at one vertex is relocated to another vertex,and characterize the unique hypergraph whose least H-eigenvalue attains the minimum among all hypergraphs in a certain class of hypergraphs which contain a fixed connected hypergraph.