  It is shown that renormalization of the Fayet-Iliopoulos term in a softly
broken SUSY gauge theory, in full analogy with all the other soft terms
renormalizations, is completely defined in a rigid or an unbroken theory.
However, contrary to the other soft renormalizations, there is no simple
differential operator that acts on the renormalization functions of a rigid
theory and allows one to get the renormalization of the F-I term. One needs an
analysis of the superfield diagrams and some additional diagram calculations in
components. The method is illustrated by the four loop calculation of some part
of renormalization proportional to the soft scalar masses and the soft triple
couplings.
