Decrease of entanglement by local operations in the D\"ur-Cirac method

One cannot always obtain information about entanglement by the D"ur-Cirac (DC) method. The impracticality is attributed to the decrease of entanglement by local operations in the DC method. We show that, even in 2–qubit systems, there exist states whose entangled property the DC method never evaluates. The class of such states in 2–qubit systems is completely characterized by the value of the fully entangled fraction. Actually, a state whose fully entangled fraction is less than or equal to 1/2 is always transformed into a separable state by local operations in the DC method, even if it has negative partial transposition.