For the basic problem of closed-loop identification, a new closed-loop identification algorithm is proposed in the framework of subspace method combined with linear algebra and geometry. In order to implement a new reconstruction of the state sequence, the output and input error sequences are included in the input subspace based on the augmented input. The estimation error, which is produced by open-loop algorithm when it is applied in the existence of feedback, is eliminated. The consistency estimate of system state-space matrices is implemented and the consistency property is proven in theory. Finally, the efficiency of this method is illustrated with a simulation example.