The well-accepted Nelson-Seiberg theorem relates R-symmetries to
supersymmetry (SUSY) breaking vacua, and provides a guideline for SUSY model
building which is the most promising physics beyond the Standard Model. In the
case of Wess-Zumino models with perturbative superpotentials, we revise the
theorem to a combined necessary and sufficient condition for SUSY breaking
which can be easily checked before solving the vacuum. The revised theorem
provides a powerful tool to construct either SUSY breaking or SUSY vacua, and
offers many practicable applications in low energy SUSY model building and
string phenomenology.Comment: 5 pages; v2: abstract and introduction revised; v3: condition of
perturbative superpotentials added, JHEP published versio