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This correspondence develops a novel and efficient algorithm to recursively extract multiple minor components from an N-dimensional vector sequence. This algorithm is of computational complexity O(N2)and obtained by approximating the well-known inverse-power iteration in conjunction with Galerkin method. Moreover, the convergence speed of the proposed algorithm is faster than that of the stochastic gradient-based algorithms with complexity O(Ngamma), where gamma is the number of minor components. Global convergence of the proposed algorithm is established. Unlike the classical recursive-least-squares-type algorithms (Ljung and Ljung, Automatica, 1985), it is shown by simulations that the proposed algorithm may have good numerical stability over a very large data sequence due to no use of the well-known matrix inversion lemma.