  We adopt a superspace/supergraph formalism to pursue the investigation of the
structure of one- and two-loop divergences in the frame of the minimal
O'Raifeartaigh model that realizes the F-term spontaneous supersymmetry
breaking. The linear delta expansion(LDE) procedure is introduced and
renormalization is carried out up to the second order in the LDE expansion
parameter. In agreement with the nonrenormalization theorem for the
(chiral/antichiral) matter potential of ${\mathcal N}=1, \ D=4$ supersymmetry,
our explicit supergraph calculations confirm that only the K\"{a}hler potential
is actually renomalized.
