  We propose a protocol ${\cal D}_n$ for faithfully teleporting an arbitrary
$n$-qudit state with the tensor product state (TPS) of $n$ generalized Bell
states (GBSs) as the quantum channel. We also put forward explicit protocol
${\cal D}'_n$ and ${\cal D}''_n$ for faithfully teleporting an arbitrary
$n$-qudit state with two classes of $2n$-qudit GESs as the quantum channel,
where the GESs are a kind of genuine entangled states we construct and can not
be reducible to the TPS of $n$ GBSs.
