Lapointe, L. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile.The supersymmetric extension of a model introduced by Lukierski, Stichel, and Zakrewski in the non-commutative plane is studied. The Noether charges associated to the symmetries are determined. Their Poisson algebra is investigated in the Ostrogradski-Dirac formalism for constrained Hamiltonian systems. It is shown to provide a supersymmetric generalization of the Galilei algebra with a two-dimensional central extension.