A self-stabilizing and unified algorithm is introduced to extract the eigen-pairs of a covariance matrix.The proposed algorithm is available for both principal component analysis(PCA) and minor component analysis(MCA) by simply altering the sign, and can estimate the corresponding eigenvalue from the norm of the estimated eigenvector, which can realize the eigen-pair extraction.The convergence analysis of the proposed algorithm based on the deterministic discrete time(DDT) approach is evaluated and the condition for convergence is also given.Finally, compared with existing algorithms, the convergence of the proposed algorithm is verified by the simulations.