  It is commonly believed that unbroken supersymmetry (SUSY) implies that all
members of a supermultiplet have the same mass. We demonstrate that this is not
true, by exhibiting a simple counterexample. We employ the formalism of
homeotic fermions, in a simple model where CPT conjugate fermions have
different masses. This model can be supersymmetrized to a hypermultiplet of
fields which form a representation of the conventional N=2 SUSY algebra.
Nevertheless, CPT conjugate states in this hypermultiplet have different
masses. These surprising results do not violate either the CPT theorem nor the
Haag-Lopuszanski-Sohnius theorem.
