  We study the gauge symmetry breaking of an ${\cal N}=1$ supersymmetric
Yang-Mills theory defined on $M^4\times S^1$, taking correctly account of the
vacuum expectation values for the adjoint scalar field $\vev{\Sigma}$ in vector
multiplet in addition to the Wilson line phases $\vev{A_y}$. We evaluate the
one-loop effective potential and obtain the vacuum configuration, for which an
SU(N) gauge symmetry is not broken. In case of an orbifold $S^1/Z_2$, under
appropriate orbifolding boundary conditions, two Higgs doublets are embedded in
the zero modes, $A_y^{(0)}$ and $\Sigma^{(0)}$. We point out that the
tree-level scalar potential resulted from the covariant derivative for the
adjoint scalar field is identical to the $D$-term of the MSSM. We also briefly
mention the mass spectra of the gauge and Higgs sector in the theory.
