  The form of the most general orbifold breaking of gauge, global and
supersymmetries with a single extra dimension is given. In certain theories the
Higgs boson mass is ultraviolet finite due to an unbroken local supersymmetry,
which is explicitly exhibited. We construct: a 1 parameter SU(3) \times SU(2)
\times U(1) theory with 1 bulk Higgs hypermultiplet, a 2 parameter SU(3) \times
SU(2) \times U(1) theory with 2 bulk Higgs hypermultiplets, and a 2 parameter
SU(5) \to SU(3) \times SU(2) \times U(1) theory with 2 bulk Higgs
hypermultiplets, and demonstrate that these theories are unique. We compute the
Higgs mass and compactification scale in the SU(3) \times SU(2) \times U(1)
theory with 1 bulk Higgs hypermultiplet.
