Energetic ion excited non-resonant fishbone-like modes (FLMs) of m / n > 1 is investigated for reversed magnetic shear configurations. It is found that the mode can be destabilized by trapped fast ions with a similar excitation mechanism as m / n = 1 fishbones but with a local interchange-like mode structure, which is in agreement with previous experiments (Toi et al 1999 Nucl. Fusion39 1929). The dispersion relation of the mode is derived for m / n > 1. The radial mode structure is then studied by numerically solving the eigenvalue equation. Effects of on/off-axis heating, the width of the particle distribution, the beam energy and the energy distribution on the mode are discussed in detail. Nonlinear analysis of the mode is also carried out by a modified predator–prey model.