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In this paper,we study the topology of moment-angle manifolds and prove a conjecture of S.Gitler and S.López de Medrano concerned with the behavior of the moment-angle manifold under the surgery 'cutting off a vertex' on a simple polytope.Let P be a simple polytope of dimension n with m facets and Pv be a polytope obtained from P by cutting off one vertex v.Let Z =Z(P) and Zv =Z(Pv) be the corresponding moment-angle manifolds.S.Gitler and S.L6pez de Medrano conjectured that: Zv is diffeomorphic to (a)[(Z -Dn+m) × D2]# #m-nj=-1n (m-nj)(Sj+2 × Sm+n-j-1),and they proved the conjecture in the case m ＜ 3n.In this paper we prove the conjecture in the general case.