  Recently we proposed an attractive scenario of grand unified theories with
anomalous $U(1)_A$ gauge symmetry, in which doublet-triplet splitting is
naturally realized in SO(10) unification using Dimopoulos-Wilczek mechanism and
realistic quark and lepton mass matrices can be obtained in a simple way. In
this paper we show that there is a mechanism in which the doublet Higgs obtains
the supersymmetric mass which is proportional to the SUSY breaking parameters.
This mechanism can be applied easily in the above scenario. The point is that
the mass term, which is forbidden by SUSY zero mechanism, can be induced by
SUSY breaking. The proportional coefficient is controlled by the anomalous
U(1)_A charges.
