  In this paper we investigate iterative roots of strictly monotone upper
semi-continuous multifunctions having finitely many jumps. Known results are
concerning roots of order 2 for multifunctions of exact one jump. For the
general investigation, we introduce a concept `intensity' to formulate the
growth of jumps under iteration and find a class of strictly monotone and upper
semi-continuous multifunctions of intensity 1, called exclusive multifunctions,
each of which has an absorbing interval. Then we use the absorbing interval to
construct iterative roots of order $n$ for those exclusive multifunctions.
