Computing free vibration properties such as natural frequencies and mode shapes of fluid-structure interaction (FSI) systems leads to a special type of asymmetric eigen-problems. Standard methods for solving symmetric eigenvalue problems cannot be applied directly for solving these asymmetric problems and should be modified. The pseudo symmetric subspace iteration method is a well-known method in this field which uses symmetric matrices instead of original asymmetric ones. However, this method is not so efficient in computing high number eigenpairs of the fluid structure systems (say > 40). Accelerated pseudo symmetric subspace iteration method increases the efficiency of the basic method utilizing constant size subspace and shifting technique. However, this method uses a very conservative shifting value, which is always smaller than last converged eigenvalue. In this study, an aggressive shifting technique which selects shifting value larger than converged eigenvalues and near unconverged eigenvalues, is proposed to solve the asymmetric eigen-problems. This technique improves efficiency of the accelerated pseudo symmetric subspace iteration method by 30 to 40 percent. Also, a computable error bound is proposed as convergence criterion for the asymmetric eigen-problems. This error bound, on the one hand, guarantees the accuracy of the converged eigen values and, on the other hand, gives an approximate range for unconverged values. This error bound is necessary to select the shifting value in the aggressive technique. In this paper, previous methods were studied first and then the proposed method is investigated and examined by several practical examples.