  We propose a simple geometrical approach for finding the Lewenstein-Sanpera
decomposition of Bell decomposable states of 2 otimes 2 quantum systems. We
show that in these systems, the weight of the pure entangled part in the
decomposition is equal to the concurrence of the state. It is also shown that
the optimized separable part of L-S decomposition minimizes the von Neumann
relative entropy. We also obtain the decomposition for a class of mixed states
by using some LQCC actions. It is also shown that for these states the average
concurrence of L-S decomposition is equal to their concurrence.
