The stability of the fishbone mode in the presence of trapped energetic ions in plasmas of spherical tokamaks is investigated. It hasbeen shown that, when plasma β is sufficiently high toresult in a magnetic valley in the equilibrium magnetic field,the fishbone mode is stable due to the inversion of direction ofthe toroidal precession. This result is valid for both highfrequency and low frequency fishbone branches. It is based ongeneral qualitative analysis and calculations involving asuggested analytical expression for the equilibrium magneticfield and calculated bounce and precessional frequencies of theenergetic ions. Stability conditions are obtained which agree withexperimental observations.