  Entanglement and Bell nonlocality are used to describe quantum
inseparabilities. Bell-nonlocal states form a strict subset of entangled
states. A natural question arises concerning how much territory Bell
nonlocality occupies entanglement for a general two-qubit entangled state. In
this work, we investigate the relation between entanglement and Bell
nonlocality by using lots of randomly generated two-qubit states, and give out
a constraint inequality relation between the two quantum resources. For
studying the upper or lower boundary of the inequality relation, we discover
maximally (minimally) nonlocal entangled states, which maximize (minimize) the
value of the Bell nonlocality for a given value of the entanglement.
Futhermore, we consider a special kind of mixed state transformed by performing
an arbitrary unitary operation on werner state. It is found that the special
mixed state's entanglement and Bell nonlocality are related to ones of a pure
state transformed by the unitary operation performed on the Bell state.
