Mechanical metamaterials can be used to control wave propagation because they are flexibly adjustable. In this paper, a one-dimensional rotor-in-rotor metamaterial with internal rotor coupling is proposed. This metamaterial introduces a new connection between lattices into a rotor-in-rotor system to produce a nonlocal metamaterial. Meanwhile, a zero-frequency bandgap with negative mass can be obtained. The vibration reduction efficiency of bandgaps is analysed based on the recursive method and numerically verified. Furthermore, wave splitting is found in the rotor-in-rotor metamaterial due to strong equivalent nonlocal interactions. Its dispersion relation shows a “dual wavevector” phenomenon: there are frequency ranges where a positive slope and a negative slope coexist. Numerical simulations using finite cell analysis are performed to validate the wave splitting by calculating the phase velocity and group velocity. The finding of wave splitting in the dual wavevector region is expected to provide new insights to control wave propagation.