  Consider an exact couple in a semiabelian category in the sense of Palamodov,
i.e., in an additive category in which every morphism has a kernel as well as a
cokernel and the induced morphism between coimage and image is always monic and
epic. Assume that the morphisms in the couple are strict, i.e., they induce
even isomorphisms between their corresponding coimages and images. We show that
the classical construction of Eckmann and Hilton in this case produces two
derived couples which are connected by a natural bimorphism. The two couples
correspond to the a priori distinct cohomology objects, the left resp. right
cohomology, associated with the initial exact couple. The derivation process
can be iterated under additional assumptions.
