A stochastic realization problem of a stationary stochastic process is re-visited, and a new stochastically balanced realization algorithm is derived in a Hilbert space generated by second-order stationary processes. The present algorithm computes a stochastically balanced realization by means of the singular value decomposition of a weighted block Hankel matrix derived by a "block LQ decomposition". Extension to a stochastic subspace identification method explains how the proposed abstract algorithm is implemented in system identification. (c) 2006 Elsevier Ltd. All rights reserved.