  The quantization of the electroweak theory is performed starting from the
Lagrangian given in the so-called unitary gauge in which the unphysical
Goldstone fields disappear. In such a Lagrangian, the unphysical longitudinal
components of the gauge fields and the residual gauge degrees of freedom are
naturally eliminated by introducing the Lorentz gauge condition and the ghost
equation. In this way, the quantum theory given in $\alpha $-gauge is perfectly
established in the Lagangian formalism by the Faddeev-Popov approach or the
Lagrange multiplier method in the framework of SU(2)$\times $U(1) gauge
symmetry. The theory established is not only simpler than the ordinary
R$_\alpha -$gauge theory, but also explicitly renormalizable. The unitarity of
the S-matrix is ensured by the $\alpha -$limiting procedure proposed
previously. Especially, it is shown that the electroweak theory without
involving the Higgs boson can equally be formulated whitin the $SU(2)\times
U(1)$ symmetry and exhibits good renormalizability. The unitarity of such a
theory may also be guaranteed by the $\alpha $-limiting procedure.
