  Based on the assumption that the receiver Bob can apply any unitary
transformation, Horodecki {\it et al.} [Phys. Lett. A {\bf 222}, 21 (1996)]
proved that any mixed two spin-1/2 state which violates the Bell-CHSH
inequality is useful for teleportation. Here, we further show that any X state
which violates the Bell-CHSH inequality can also be used for nonclassical
teleportation even if Bob can only perform the identity or the Pauli rotation
operations. Moreover, we showed that the maximal difference between the two
average fidelities achievable via Bob's arbitrary transformations and via the
sole identity or the Pauli rotation is 1/9.
