  Mixed spin-1/2 states violating Bell-CHSH inequality is useful for
teleportation. There exist states which do not violate Bell-inequality but is
still useful as teleportation channels. Maximally entangled mixed states of
Munro class and Ishizaka-Hiroshima class are such types which although satisfy
Bell-CHSH inequality, yet can perform better as teleportation channels for a
given degree of mixedness\cite{adhikari2010}. In this work we construct class
of mixed states of non-maximally entangled types whose efficacy as
teleportation channels have been studied. For certain range of state
parameters, these non-maximally entangled mixed states performs better as
quantum teleportation channels than certain maximally entangled mixed states
(such as Werner state). These constructed states, though entangled, satisfy
Bell-CHSH inequality implying further that violation of local inequalities may
not be good indicators of their ability to complete quantum processing tasks
such as teleportation.
