D0 and D1 Brane With $\kappa_-$ and $\kappa_+$ Extended Symmetry

D0 brane (D-particle) and D1 brane actions possess first and second class constraints that result in local $\kappa$ symmetry. The $\kappa$ symmetry of the D-particle and the D1 brane is extended here into a larger symmetry ($\kappa_-$ and $\kappa_+$) in a larger phase space by turning second class constraints into first class. Different gauge fixings of these symmetries result in different presentations of these systems while a "unitary" gauge fixing of the new $\kappa_+$ symmetry retrieves the original action with $\kappa_- = \kappa$ symmetry. For D1 brane our extended phase space makes all constraints into first class in the case of vanishing world sheet electric field (namely $(0, 1)$ string).