  When the supersymmetric theory contains the ``anomalous" $U(1)$ gauge
symmetry with Green-Schwarz anomaly cancellation mechanism in 4 dimensions, its
Fayet-Iliopoulos $D$-term generates non-universal scalar masses and the
positive cosmological constant after the supersymmetry breaking. Both give the
new contributions to the known results from $F$-term. Our mechanism is
naturally realized in many string models and in some cases, leads to remarkable
cancellations between $F$- and $D$-term contributions, providing the universal
scalar mass and vanishing cosmological constant. We illustrate how such a
possibility can arise by taking a simple orbifold example.
