In the well known paper of Rosenbluth, Krall and Rostoker it has been shown that plasma flute instability can be absent if the ion Larmor radius is not too small. At the same time, however, it follows from ref. 4 that for a sufficiently remote metallic housing, the mode m = 1 does not stabilize even when all other perturbations are intentionally stabilized. This article is devoted to further analysis of this problem. In particular, the necessary and sufficient conditions are found for which first-mode instability is possible. In addition to remoteness of housing two other conditions must be fulfilled: (1) density n, pressure p and radius of curvature R must be linked by the relation (Rr)−1 ∂p/∂n≈const; (2) away from the center, density must decrease faster than 1/r2. If only one of these conditions is not fulfilled, and the plasma is not too dilute (CA2≪C2) the stabilization effect occurs even for a perturbation with m = l. This paper gives an example of a distribution that is stable with respect to perturbations with any m.