Abstract: A new improved algorithm of simultaneous iteration is presented for evaluation of generalized eigenproblems in dynamic analysis of large structures.The convergence of this algorithm is proved by the concepts of EK subspace and eigendirection and some details of how to perform this algorithm in computer are discussed.Based on statistics of computational quantity required for each step of iteration and a great number of practical computations, it is shown that in convergence rate the present method is comparable to some simultaneous or subspace iteration algorithms available up to now, but it can cut down the computer run time for each step of iteration and raise the computation efficiency.