The spectrum of open strings on various non-BPS D-brane configurations in type II string theory on a K3 orbifold is analysed. At a generic point in the corresponding moduli space the spectrum of open strings does not have any degeneracy between bosonic and fermionic states. However, there exist special values for these moduli for which many non-BPS D-brane configurations have an exactly Bose-Fermi degenerate open string spectrum at all mass levels. In this case the closed string exchange interaction between a pair of such D-brane configurations vanishes at all distances.