  Consistent boundary Poisson structures for open string theory coupled to
background $B$-field are considered using the new approach proposed in
hep-th/0111005. It is found that there are infinitely many consistent Poisson
structures, each leads to a consistent canonical quantization of open string in
the presence of background $B$-field. Consequently, whether the $D$-branes to
which the open string end points are attached is noncommutative or not depends
on the choice of a particular Poisson structure.
