Generalized minor component analysis(GMCA) has played a vital role in many areas of the modern signal processing. Up to now, few algorithms can possess four properties together, which are the information criterion corresponding to the algorithm, convergence property, self-stabilizing property and ability of extracting multiple generalized minor components. To deal with this problem, a novel information criterion is proposed and based on the criterion, a generalized minor component extraction algorithm is derived. Then, the global convergence of the algorithm is analyzed using the deterministic discrete time method. Besides, self-stabilizing property is illustrated through theorical researching on the relationship between the convergence ability and initial state of the algorithm. Furthermore, the application of the algorithm in multiple GMCs extraction is exploved. In contrast with the existing algorithms, the proposed algorithm is superior in convergence speed. The properties of the algorithm are verified by simulations in Matlab.