  By considering the decomposition of a generic two qubit density matrix
presented by Wootters [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245 (1998)],
the robustness of entanglement for any mixed state of two qubit systems is
obtained algebraically. It is shown that the robustness of entanglement is
proportional to concurrence and in Bell decomposable density matrices it is
equal to the concurrence. We also give an analytic expression for two separable
states which wipe out all entanglement of these states. Since thus obtained
robustness is function of the norm of the vectors in the decomposition we give
an explicit parameterization for the decomposition.
