  We study the lattice model for the supersymmetric Yang-Mills theory in two
dimensions proposed by Cohen, Kaplan, Katz, and Unsal. We re-examine the formal
proof for the absence of susy breaking counter terms as well as the stability
of the vacuum by an explicit perturbative calculation for the case of U(2)
gauge group. Introducing fermion masses and treating the bosonic zero momentum
mode nonperturbatively, we avoid the infra-red divergences in the perturbative
calculation. As a result, we find that there appear mass counter terms for
finite volume which vanish in the infinite volume limit so that the theory
needs no fine-tuning. We also find that the supersymmetry plays an important
role in stabilizing the lattice space-time by the deconstruction.
