This article is concerned with a novel data-driven bias-eliminated subspace identification approach for closed-loop systems. Compared with the existing methods, the proposed method first proposes to utilize the coprime factorization of the controller to construct an instrumental variable uncorrelated with noise under closed-loop conditions. Furthermore, it can reliably eliminate the pole estimation bias due to the correlation between inputs and noise under feedback control. More importantly, the proposed method establishes a general framework for both open-loop and closed-loop system identification. Performance comparisons with two other closed-loop methods are made from many different aspects. Finally, the performance of the identified system is again demonstrated in the vehicle lateral dynamic system.