  Let $ k, n \in \mathbb{N}^+ $ and $ m \in \mathbb{N}^+ \cup \{\infty \} $. A
$ k $-multiset in $ [n]_m $ is a $ k $-set whose elements are integers from $
\{1, 2, \ldots, n\} $, and each element is allowed to have at most $ m $
repetitions. A family of $ k $-multisets in $ [n]_m $ is said to be
intersecting if every pair of $ k $-multisets from the family have non-empty
intersection. In this paper, we give the size and structure of the largest
non-trivial intersecting family of $ k $-multisets in $ [n]_m $ for $ n \geq k
+ \lceil k/m \rceil $. In the special case when $m=\infty$, our result gives
rise to an unbounded multiset version for Hilton-Milner Theorem given by
Meagher and Purdy. Furthermore, our main theorem unites the statements of the
Hilton-Milner Theorem for finite sets and unbounded multisets.
