Supersymmetry does not imply mass degeneracy

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 or the Haag¿Lopuszański¿Sohnius theorem.