Throughout this paperLdenotes a Hopf algebra over the ground fieldkwith a bijective antipodeSL, andHdenotes a Hopf algebra in the Yetter-Drinfeld categoryWe prove the fundamental theorem for rightH-Hopf modules in. We also show that ifHis finite dimensional, itsk-dualH*has a rightH-Hopf module structure which is not analogous to usual one. As an application we give a direct proof of the [FMS] result: ifHis finite-dimensional, then it is a Frobeniusk-algebra. We also imply the [FMS] description of the dual bases forH