By using so-called preconditioning algorithms, it has been successful to solve PDE discrete algebraic systems in high performance computations. However, the potential of PDE eigen-problem solver is still far from expected. It is well-known that from the fundamental algebraic theorem, any n?degree polynomial can be decomposed into a product with several lower degree, such as quadratic polynomials, and linear terms. Therefore, by using some characteristic transforms, such as discrete Fourier, it is possible to decouple the original high order eigen-problem into some lower eigen-problems in parallel. In this paper, we take a cubic Hermite-interpolation as an example, an algorithm of Double-Decoupling Subspaces for Solving FEM Eigen-problems is proposed for solving a class of discrete elliptic generalized eigen-problems. Performance has been raised obviously, comparing with the traditional algorithm: turn to ordinary eigen-problem first, then do diagonalization at once. Moreover, the new algorithm can judge spurious-free and prevent from spurious eigenvalues.