The Coulomb gauge has a long history and many uses. It is especially u
seful in bound state applications. An important feature of this gauge
is that the matter fields have an infrared finite propagator in an on-
shell renormalisation scheme. This is, however, only the case if the r
enormalisation point is chosen to be the static point on the mass-shel
l, p = (m, 0, 0, 0). In this letter we show how to extend this key pro
perty of the Coulomb gauge to an arbitrary relativistic renormalisatio
n point. This is achieved through the introduction of a new class of g
auges of which the Coulomb gauge is a limiting case. A physical explan
ation for this result is given.