  Nonanticommutativity in an open super string moving in the presence of a
background antisymmetric tensor field $\mathcal{B}_{\mu \nu}$ is investigated
in a conformal field theoretic approach, leading to nonanticommutative
structures. In contrast to several discussions, in which boundary conditions
are taken as Dirac constraints, we first obtain the mode algebra by using the
newly proposed normal ordering, which satisfies both equations of motion and
boundary conditions. Using these the anticommutator among the fermionic string
coordinates is obtained. Interestingly, in contrast to the bosonic case, this
new normal ordering plays an important role in uncovering the underlying
nonanticommutative structure between the fermionic string coordinates. We feel
that our approach is more transparent than the previous ones and the results we
obtain match with the existing results in the literature.
