  We study the principles of the gauge symmetry and supersymmetry breaking due
to the local or global discrete symmetries on the extra space manifold. We show
that the gauge symmetry breaking by Wilson line is the special case of the
discrete symmetry approach where all the discrete symmetries are global and act
freely on the extra space manifold. As applications, we discuss the N=2
supersymmetric SO(10) and $E_8$ breaking on the space-time $M^4\times A^2$ and
$M^4\times D^2$, and point out that similarly one can study any N=2
supersymmetric $SO(M)$ breaking. We also comment on the one-loop effective
potential, the possible questions and generalization.
