Abstract: Fast and effective decomposition of subspace is important to the engineering application of subspace-based algorithms.A new form of the desired signal is presented,and that in the context of space-time white noise the Krylov subspace of both the covariance matrix of the observation signal and the crosscorrelation vector between the observation signal and the desired signal is equivalent to the signal subspace is proved,thus the fast estimation of signal subspace can be realized by computing the basis of the Krylov subspace with the multi-stage Wiener filter(MSWF).By simulation,it is clear that the proposed method can perform the fast subspace decomposition effectively,especially in the case of lower signal to noise ratio.