We present an exact formula for the beta-function for the soft-breakin
g scalar mass in an N=1 supersymmetric gauge theory, in the form of an
operator acting on the anomalous dimension. In particular we give the
exact form for the correction due to the epsilon-scalar mass, and sho
w that it has a particularly simple form in the renormalisation scheme
corresponding to the exact NSVZ gauge beta-function. (C) 1998 Elsevie
r Science B.V. All rights reserved.