Tuned vibration neutralisers are used to suppress the vibration of a host structure subjected to external harmonic forces. Although they are analogous to tuned vibration absorbers, the primary difference is that while absorbers are usually designed with optimum damping to attenuate vibration in a frequency range around a resonance, neutralisers are designed with relatively low damping to act as a mechanical notch-filter. The narrow band frequency in which the conventional neutralisers are effective, and the mistuning compromising their performance, are known problems. Thus, self-tuning vibration neutralisers were introduced to make them more robust. In many cases, however, these systems need an external power source to adapt. This paper concerns an investigation into a self-tuning vibration neutraliser for two distinct frequencies, that does not need an external power source. It consists of a rectangular beam with tip masses, which is held at its centre in a roller bearing that is fixed to a host structure. The rectangular cross section has two different stiffnesses in the local coordinates that can rotate with respect to the global reference. Results from some experimental tests compare very well with time domain numerical simulations. It is shown that the coupling between two orthogonal degrees-of-freedom enables the neutraliser to passively tune to one of two tuned frequencies, depending on the frequency of the external harmonic force.