Decrease of entanglement by local operations in the Dur-Cirac method

One cannot always obtain information about entanglement by the Dur-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.