We propose a new nonperturbative test for supersymmetry breaking. The test is first to break supersymmetry by introducing a lattice and then to study the behavior of the ground-state energy as a function of the lattice spacing a. We assume that as a approaches zero, E/sub 0/approx.ca/sup ..gamma../, where c is a nonzero constant and ..gamma.. is a critical exponent. If ..gamma.. is positive as a..-->..0, the ground-state energy of the continuum theory is zero and the theory is supersymmetric. On the other hand, if ..gamma.. is zero or negative, then supersymmetry is broken. We verify this test in the context of supersymmetric quantum mechanics using a strong-coupling expansion to calculate E/sub 0/ and ..gamma... We find that for the supersymmetric version of g/sup 2/x/sup 6/ quantum mechanics, ..gamma.. = 1.16 +- 0.02, whereas ..gamma.. is consistent with zero when we consider the supersymmetric extension of g/sup 2/x/sup 4/ theory.