Radiofrequency fields launched in the ion Bernstein mode in a plasma can stabilize the interchange mode by coupling it to ion Bernstein wave side-bands. A kinetic theory for non-linear coupling, based on the guiding centre formalism, is developed and conditions for stabilization are derived. Waves with ω0 > ωci, k0⊥ vi/ωci ⪆ 1 are better suited for stabilization.