This paper presents an innovative eigenvalue solution technique that leverages an enhanced Gram-Schmidt procedure to improve the efficiency and stability of QR-based methods. Among iterative techniques—such as vector, polynomial, and subspace iterations—transformation methods generally demonstrate superior performance. Specifically, the Jacobi and Householder QR methods are well-established in finite element analysis due to their high computational efficiency. Although the Householder QR method is preferred for larger systems owing to its initial reduction of the matrix to tridiagonal form, it possesses a critical drawback: the reduction process increases the bandwidth of the unreduced matrix, thereby disrupting the efficient exploitation of the original banded structure of matrix K. To overcome this limitation, we propose an enhanced version of the Gram-Schmidt procedure. Unlike the standard Modified Gram-Schmidt (MGS) algorithm, our approach incorporates a strategic projection mechanism that significantly mitigates the loss of orthogonality, particularly in ill-conditioned systems. This method supports matrices of various dimensions and promotes rapid convergence in the tested scenarios. Comparative studies demonstrate that the proposed technique yields solutions of comparable accuracy while significantly reducing computation time. Numerical experiments conducted on two structural examples and one random symmetric ill-conditioned matrix confirm that the proposed technique is both efficient and robust.