  Discontinuity of gauge theory in the gauge condition $n\cdot\partial n\cdot
A=0$, which emerges at $n\cdot k=0$, is studied here. Such discontinuity is
different from that one confronts in axial gauge and can not be regularized by
conventional analytical continuation method. The Faddeev-Popov determinate of
the gauge $n\cdot\partial n\cdot A=0$, which is solved explicitly in the
manuscript, behaves like a $\delta$-functional of gauge potentials once
singularities in the functional integral is neglected and the length along
$n^{\mu}$ direction of the space tends to infinity. As a sequence, perturbation
series in the gauge $n\cdot\partial n\cdot A=0$ returns to that in axial gauge
for short-range correlated objects that are free from singularities in path
integral. However, the equivalence between the gauge $n\cdot\partial n\cdot
A=0$ and axil gauge is nontrivial for long-range correlated objects and
quantities that are affected by singularities in path integral. Continuity of
gauge links one encounter in perturbation theory and lattice calculation is
affected by such discontinuity.
