A key question concerning the three-body fragmentation of polyatomic molecules is the distinction of sequential and concerted mechanisms, i.e., the stepwise or simultaneous cleavage of bonds. Using laser-driven fragmentation of OCS into O^{+}+C^{+}+S^{+} and employing coincidence momentum imaging, we demonstrate a novel method that enables the clear separation of sequential and concerted breakup. The separation is accomplished by analyzing the three-body fragmentation in the native frame associated with each step and taking advantage of the rotation of the intermediate molecular fragment, CO^{2+} or CS^{2+}, before its unimolecular dissociation. This native-frame method works for any projectile (electrons, ions, or photons), provides details on each step of the sequential breakup, and enables the retrieval of the relevant spectra for sequential and concerted breakup separately. Specifically, this allows the determination of the branching ratio of all these processes in OCS^{3+} breakup. Moreover, we find that the first step of sequential breakup is tightly aligned along the laser polarization and identify the likely electronic states of the intermediate dication that undergo unimolecular dissociation in the second step. Finally, the separated concerted breakup spectra show clearly that the central carbon atom is preferentially ejected perpendicular to the laser field.