  The problem of an open string in background $B$-field is discussed. Using the
discretized model in details we show that the system is influenced by infinite
number of second class constraints. We interpret the allowed Fourier modes as
the coordinates of the reduced phase space. This enables us to compute the
Dirac brackets more easily. We prove that the coordinates of the string are
non-commutative at the boundaries. We argue that in order to find the Dirac
bracket or commutator algebra of the physical variables, one should not expand
the fields in terms of the solutions of the equations of motion. Instead, one
should impose the set of constraints in suitable coordinates.
