  D\"{u}r [Phys. Rev. Lett. {\bf 87}, 230402 (2001)] constructed $N$-qubit
bound entangled states which violate a Bell inequality for $N\ge 8$, and his
result was recently improved by showing that there exists an $N$-qubit bound
entangled state violating the Bell inequality if and only if $N\ge 6$ [Phys.
Rev. A {\bf 79}, 032309 (2009)]. On the other hand, it has been also shown that
the states which D\"{u}r considered violate Bell inequalities different from
the inequality for $N\ge 6$. In this paper, by employing different forms of
Bell inequalities, in particular, a specific form of Bell inequalities with $M$
settings of the measuring apparatus for sufficiently large $M$, we prove that
there exists an $N$-qubit bound entangled state violating the $M$-setting Bell
inequality if and only if $N\ge 4$.
