A new kind of fishbone instability associated with circulating energetic ions is predicted. The considered instability is essentially the energetic particle mode; it is characterized by m/n not equal to 1 (m and n are the poloidal and toroidal mode numbers, respectively). The mode is localized inside the flux surface where the safety factor (q) is q* = m/n, its amplitude being maximum near q*. The instability arises in plasmas with small shear inside the q* surface and q(0) > 1. A possibility to explain recent experimental observations of the m = 2 fishbone oscillations accompanied by strong changes of the neutron emission during tangential neutral-beam injection in the National Spherical Torus Experiment [M. Ono, et al., Nucl. Fusion 40 (2000) 557] is shown.