  We show how to teleport reliably an arbitrary superposition of n=0 and n=1
vibrational number state between two distant ions. This is done by first
mapping the vibrational state to be teleported into the internal degrees of
freedom of a given ion. Then we handle with the internal superposition state
following Bennett's original protocol and a recently proposed technique for
teleportation of ionic internal states [quant-ph/9903029]. Finally, the
teleportation of the vibrational state is achieved by reversing the mapping
process in the receiver ion. We remark that as in the teleportation of cavity
field and atomic states, the teleportation of vibrational states is 100%
successful for an ideal process.
