A new stochastic subspace identification algorithm is developed with the help of a stochastic realization on a finite interval. First, a finite-interval realization algorithm is re-derived via "block-LDL decomposition" for a finite string of complete covariance sequence. Next, a stochastic sub-space identification method is derived by adapting the finite-interval realization algorithm to incomplete covariance matrices defined by a finite time-series data. The proposed sub-space identification method always works, and computes a stochastic model from the "block-LQ decomposition" without solving any Riccati equations.