  The Lewenstein-Sanpera decomposition for a generic two-qubit density matrix
is obtained by using Wootters's basis. It is shown that the average concurrence
of the decomposition is equal to the concurrence of the state. It is also shown
that all the entanglement content of the state is concentrated in the
Wootters's state $|x_1>$ associated with the largest eigenvalue $\lambda_1$ of
the Hermitian matrix $\sqrt{\sqrt{\rho}\tilde{\rho}\sqrt{\rho}}$ >. It is shown
that a given density matrix $\rho$ with corresponding set of positive numbers
$\lambda_i$ and Wootters's basis can transforms under $SO(4,c)$ into a generic
$2\times2$ matrix with the same set of positive numbers but with new Wootters's
basis, where the local unitary transformations correspond to $SO(4,r)$
transformations, hence, $\rho$ can be represented as coset space
$SO(4,c)/SO(4,r)$ together with positive numbers $\lambda_i$. By giving an
explicit parameterization we characterize a generic orbit of group of local
unitary transformations.
