Finite element analysis is a standard tool for deterministic or probabilistic design optimization of dynamic systems. The optimization process requires repeated eigenvalue analyses which can be computationally expensive. Several reanalysis techniques have been proposed to reduce the computational cost including Parametric Reduced Order Modeling (PROM), Combined Approximations (CA), and the Modified Combined Approximations (MCA) method. Although the cost of reanalysis is substantially reduced, it can still be high for models with a large number of degrees of freedom and a large number of design variables. Reanalysis methods use a basis composed of eigenvectors from both the baseline and the modified designs which are in general linearly dependent. To eliminate the linear dependency and improve accuracy, Gram Schmidt orthonormalization is employed which is costly itself. In this paper, we propose a method to reduce the orthonormalization cost and improve the computational efficiency of the PROM reanalysis method. Our method eliminates non-important design variables and/or reduces the basis size by eliminating redundant modes. A vibratory analysis of an automotive door demonstrates the efficiency and accuracy of the proposed method.