An e-cient higher order MLFMA is developed by using an \extended-tree. With this extended-tree, the size of the box at the flnest level is reduced, and the cost associated with the aggregation and disaggregation operations is signiflcantly decreased. The sparse approximate inverse (SAI) preconditioner is utilized to accelerate the convergence of iterative solutions. The Cholesky factorization, instead of the often used QR factorization, is employed to construct the SAI preconditioner for cavity scattering analysis, by taking advantage of the symmetry of the matrix arising from electric fleld integral equation. Numerical experiments show that the higher order MLFMA is more e-cient than its low-order counterpart.