  Given a discrete subgroup of the isometries of n-dimensional hyperbolic space
there is always a region kept precisely invariant under the stabilizer of a
parabolic fixed point, called the Margulis region. While in dimensions 2 and 3
this region is a horoball, it has in general a more complicated shape due to
the existence of screw parabolic elements in higher dimensions. In fact, P.
Susskind has shown that in a discrete group acting on hyperbolic 4-space
containing a screw parabolic element with irrational rotation, the
corresponding Margulis region does not contain a horoball. In this paper we
describe the asymptotic behavior of the boundary of the Margulis region when
the irrational screw parabolic is of bounded type. As a corollary we show that
the region is quasi-isometric to a horoball. Although Y. Kim has shown that two
screw parabolic isometries with irrational rotation are not conjugate by any
quasi-isometry of hyperbolic 4-space, this corollary implies that their
corresponding Margulis regions (in the bounded type case) are quasi-isometric.
