  Deterministically controllable multi-state polarizations in ferroelectric
materials are promising for the application of next-generation non-volatile
multi-state memory devices. However, the achievement of multi-state
polarizations has been inhibited by the challenge of selective control of
switching pathways. Here we report an approach to selectively control 71{\deg}
ferroelastic and 180{\deg} ferroelectric switching paths by combining the
out-of-plane electric field and in-plane trailing field in multiferroic BiFeO3
thin films with periodically ordered 71{\deg} domain wall. Four-state
polarization states can be deterministically achieved and reversibly controlled
through precisely selecting different switching paths. Our studies reveal the
ability to obtain multiple polarization states for the realization of
multi-state memories and magnetoelectric coupling based devices.
