The paper is concerned with the dynamics of large-scale wave processes in a rotating layer of inviscid conducting incompressible liquid of variable depth. The problem is modelled as a system of partial differential equations with necessary boundary conditions. With the help of auxiliary functions, the above system of partial differential magnetohydrodynamic equations is reduced to a single scalar partial differential equation. An exact analytic solution of the small perturbation problem is obtained. It is shown that if the external magnetic field is parallel to the axis of rotation of the layer, then the magnetic field decays for finite values of the magnetic Reynolds number.