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Computation of the eigenvalues with the least damping ratios is one of the most efficient approaches to analyze the electromechanical oscillations of power systems. In this paper, an improved generalized Cayley transformation (IGCT) is proposed to search the eigenvalues with an ascending order of the damping ratios efficiently. Since the proposed IGCT preserves the sparsity of the augmented state matrix with a form of DAE, the computational burden can be reduced significantly. Moreover, the eigenvalues with greater damping ratios but located near to the imaginary axis, which are usually ignored in the conventional generalized Cayley transformation, can be calculated automatically by using the proposed IGCT. A rigorous proof is presented to show the correctness and the effectiveness of the proposed method. Numerical experiments are tested on both the IEEE 118-bus system the Hainan power grid to illustrate the validity and high efficiency of the proposed method.