It is found that, in a regime in which flute oscillations are usually assumed to be stabilized effects of the finite Larmor radius, they are characterized by resonances with the ion Larmor drift. It is shown that a correct study of these resonances requires direct use of an integral equation, without expansion in the small Larmor radius. The initial value problem is solved by the method of Laplace transformation, and it is shown that the flute instabilities are indeed stable.