Matrix Model on Z-Orbifold

Six dimensional compactification of the type IIA matrix model on the ${\bf Z}$-orbifold is studied. Introducing a ${\bf Z}_{3}$ symmetry properly on the three mirror images of fields in the $N$-body system of the supersymmetric D0 particles, the action of the Matrix model compactified on the ${\bf Z}$-orbifold is obtained. In this matrix model ${\cal N}=1$ supersymmetry is explicitly demonstrated.