  A proof of Bell's theorem using two maximally entangled states of two qubits
is presented. It exhibits a similar logical structure to Hardy's argument of
``nonlocality without inequalities''. However, it works for 100% of the runs of
a certain experiment. Therefore, it can also be viewed as a
Greenberger-Horne-Zeilinger-like proof involving only two spacelike separated
regions.
