[en] It has been shown that propagation of lower hybrid rays sometimes involves cases where three types of waves are coupled through linear mode conversion in the same region of space, namely the cold lower hybrid wave, the warm lower hybrid wave, and an ion Bernstein mode. This three wave mode conversion problem is analyzed in terms of a sixth order differential equation which describes coupling between all branches, and analytic coupling coefficients are found for the case without the local absorption term. The formal solution of this equation shows that a non-trivial amount of the incident cold wave energy goes into an ion Bernstein mode, which is then absorbed by electrons via Landau damping, rather than converting into the warm branch totally, when they are closely coupled in space