  Noncommutativity in an open string moving in a background Neveu-Schwarz field
is investigated in a gauge independent Hamiltonian approach, leading to new
results. The noncommutativity is shown to be a direct consequence of the
non-trivial boundary conditions, which, contrary to several approaches, are not
treated as constraints. We find that the noncommutativity persists for all
string points. In the conformal gauge our results reduce to the usual
noncommutativity at the boundaries only.
