In addition to being observable, systems composed of interconnected subsystems must typically exhibit a particular subsystem structure, if their state is to be estimated successfully by a partition-based moving horizon estimator (PMHE). Suitable subsystem structures-also called system partitionings-can be unknown, may not be desirable for a particular application, or may not exist at all. In this contribution, we present the first PMHE without any restrictions on the system partitioning. We analyze the convergence of its iterations at each time step and the stability of its estimation error dynamics. The benefits of our solution are illustrated on a numerical example.