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We show that non-commutativity in the spacetime coordinates of D-branes, where the end points of the open strings are attached, can be obtained by modifying the canonical Poisson bracket structure, so that it is compatible with the boundary condition. In this approach, the boundary conditions are not treated as constraints. This is similar in spirit to the treatment of Hanson, Regge and Teitelboim, where modified Poison Bracketss were obtained for the free Nambu-Goto string. Those studies were, however, restricted to the case of the bosonic string and membrane only. We extend the same...