Abstract: To investigate fast retrieval of signal subspace in signal processing applications in reference to a kind of over determined low rank data matrix, the paper makes use of the relationship between left and right singular vectors of singular value decomposition, the anti power method and L D L T decomposition, and presents a fast algorithm in the retrieval of signal subspace. It obviously involues less computational complexity than is singular value decomposition, attains higher precision, and is suitable for corresponding signal processing.