  As it is well known, every bipartite $2\otimes 2$ density matrix can be
obtained from Bell decomposable states via local quantum operations and
classical communications (LQCC). Using this fact, the Lewenstein-Sanpera
decomposition of an arbitrary bipartite $2\otimes 2$ density matrix has been
obtained through LQCC action upon Lewenstein-Sanpera decomposition of Bell
decomposable states of $2\otimes 2$ quantum systems, where the product states
introduced by Wootters in [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245
(1998)] form the best separable approximation ensemble for Bell decomposable
states. It is shown that in these systems the average concurrence of the
Lewenstein-Sanpera decomposition is equal to the concurrence of these states.
