  Consider the unit ball, $B = D \times [0,1]$, containing $n$ unknotted arcs
$a_1, a_2, ..., a_n$ such that the boundary of each $a_i$ lies in $D \times
\{0\}$. The Hilden (or Wicket) group is the mapping class group of $B$ fixing
the arcs $a_1 \cup a_2 \cup ... \cup a_n$ setwise and fixing $D \times \{1\}$
pointwise. This group can be considered as a subgroup of the braid group. The
pure Hilden group is defined to be the intersection of the Hilden group and the
pure braid group.
  In a previous paper we computed a presentaion for the Hilden group using an
action of the group on a cellular complex. This paper uses the same action and
complex to calculate a finite presentation for the pure Hilden group. The
framed braid group acts on the pure Hilden group by conjugation and this action
is used to reduce the number of cases.
