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Let M be a compact symplectic manifold, and L ⊂ M be a closed Lagrangian submanifold which can be lifted to a Legendrian submanifold in the contactization of M. For any Legendrian deformation of L satisfying some given conditions, we get a new Lagrangian submanifold L . We prove that the number of intersection L ∩ L can be estimated from below by the sum of ޚ 2 -Betti numbers of L, provided they intersect transversally. MSC2000: 57R22, 53D40, 53D12, 53D10.doi:10.2140/pjm.2007.231.417 fatcat:jvjnakl5tjhtnaf4ewdg55btd4