Let G be a balanced 2-connected bipartite graph with bipartlition(X

Y). Suppose for each vertex v of G

H is the subgraph induced by the vertices which are dis- tance 2 or 3 from v

and for each vertex u which has distance 3 to v

the degree d_H(u)of uin H is at least the numbor of the vertices distance 2 from v minus(d_F(v)-2).Then Gis Hamiltonian

where the lower bound of d_H(u) is sharp.