The transfer matrix method is applied to magnetic bilayer film with the aim of expressing its characteristic equation by the interface rescaling parameters. The interface-localized mode is then shown to exist in the system for appropriately chosen values of the interface spin pinning parameters defined in the model. The authors also show that in order to achieve a proper description of the interfacial conditions in the case of bilayer 'effective interface pinning' originating in the intrinsic interfacial coupling.