  Isothermic surfaces are surfaces which allow a conformal curvature line
parametrisation. They form an integrable system, and Darboux transforms of
isothermic surfaces obey Bianchi permutability: for two distinct spectral
parameters the corresponding Darboux transforms have a common Darboux transform
which can be computed algebraically. In this paper, we discuss two-step Darboux
transforms with the same spectral parameter and show that these are obtained by
a Sym-type construction: All two-step Darboux transforms of an isothermic
surface are given, without further integration, by parallel sections of the
associated family of the isothermic surface, either algebraically or by
differentiation against the spectral parameter.
