In the refined Cayley-Arnoldi algorithm for computing critical eigenvalues of power system， the Ritz pairs are replaced by the corresponding refined Ritz pairs to form an improved algorithm. As more subspace information is contained in the refined Ritz vectors， the refined Ritz values are closer to the finally convergent Ritz values. As a result， the improved algorithm is of advantage to the convergence of the iterative computation. The Ritz pairs can be obtained cheaply and reliably with limited increase of computing time. To transfer the concerned eigenvalues within the special area on the complex plane to dominant eigenvalues， the Cayley transformation is only required once， and the adjacent eigenvalues can be obviously distinguished. The computing speed and convergence characteristic of the proposed approach are validated on three testing systems.