In this paper we consider the flute oscillation of a plasma in a helical, cylindrically symmetrical magnetic field, with shear not equal to zero, at an arbitrary value of the parameter β = 8π p/B2, particularly where β → 0. Suydam's familiar stabilization criterion loses its validity if β < (Me/Mi) (k ⊥ ϱ)2 (in a low-density plasma), and that it is replaced by the criterion θ > 4(Me/Mi)1/2 (a/R) [1 + (C/CA)2]1/2The combined stabilizing action of shear and a finite ion Larmor radius makes it possible to eliminate flute instability over the whole range of densities. (A plasma without shear, on the other hand, and with a density in the range a/R < (C/CA)2 ≳ 1 would be unstable no matter how large the Larmor radius of the ions.)