Bacterial locomotion by rotating flagella is achieved through the hook, which transmits torque from the motor to the filament. The hook is a tubular structure composed of a single type of protein, yet it adopts a curved shape. To perform its function, it must be simultaneously flexible and torsionally rigid. The molecular mechanism by which chemically identical subunits form such a dynamic structure is unknown. Here, we show the complete structure of the hook from Salmonella enterica in its supercoiled 'curved' state, at 2.9 Å resolution. Subunits in the curved hook are grouped into 11 distinctive conformations, each shared along 11 protofilaments. The domains of the elongated hook subunit behave as rigid bodies connected by two hinge regions. The reconstituted model demonstrates how identical subunits can dynamically change conformation by physical interactions while bending. These multiple subunit states contradict the two-state model, which is a key feature of flagellar polymorphism.