The stability properties of the low-frequency flute instabilities in a self-pinched ion beam propagating through a preformed plasma channel are investigated for long-wavelength and low-frequency perturbations. Consistent with the flute instabilities, the stability analysis is restricted to the surface perturbations on the ion beam. A closed algebraic dispersion relation of the flute instabilities for Bennett [Phys. Rev. 45, 890 (1934)] density profile is obtained, by making use of the energy group model. From the analytical and numerical calculations of the dispersion relation for highly collisional plasma, we find the necessary condition for instability in terms of the fractional current neutralization f. Threshold values of the fractional current neutralization for instability are tabulated for each azimuthal mode number ℓ.