  The relation between the violation of the Bell-CHSH inequalities and
entanglement properties of quantum states is not clear so one may consider the
mixedness of the system to understand the entanglement properties better than
the Bell-CHSH inequality. In this respect, we prove that if the mixedness of
the state measured by the linear entropy is less than 2/3 but strictly greater
than zero then the two qubit states are entangled. But if the linear entropy is
greater or equal to 2/3 then the state may or may not be entangled. Further we
show that our entanglement criterion detects larger set of entangled state than
Bell-CHSH inequality and Santos's entropic criterion [Phys. Rev. A 69, 022305
(2004)]. Lastly we illustrate our result by citing few examples.
