The electrostatic flute‐like normal modes were found for a collisionless loss cone plasma in a uniform magnetic field with density varying sinusoidally in one direction in space. A local method, appropriate tokL≫1, wherekis the wavenumber andLis the scale length, and a nonlocal method, appropriate tokL≲1, where both used; the ion Larmor radiusaiwas not assumed to be small. The usual drift cone mode was found whenai≪L; other instabilities were found forai≳L. In principle, the methods could be applied to other configurations of plasma.