D{u}r [Phys. Rev. Lett. {bf 87}, 230402 (2001)] constructed $N$-qubit bound entangled states which violate a Bell inequality for $Nge 8$, 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 $Nge 6$ [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 $Nge 6$. 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 $Nge 4$.
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