We propose a decentralized subspace algorithm for the identification of large-scale, interconnected systems that are described by sparse (multi) banded state-space matrices. First, we prove that the state of a local subsystem can be approximated by a linear combination of inputs and outputs of local subsystems that are in its neighborhood. Furthermore, we prove that for interconnected systems with well-conditioned, finite-time observability Gramians (or observability matrices), the size of this neighborhood is relatively small. On the basis of these results, we develop the subspace identification algorithm that identifies the state-space model of a local subsystem from the local input-output data. Consequently, the developed algorithm is computationally feasible for interconnected systems with a large number of local subsystems. Numerical results confirm the effectiveness of the new identification algorithm.