  For positive integers $n,r,k$ with $n\ge r$ and $k\ge2$, a set
$\{(x_1,y_1),(x_2,y_2),\dots,(x_r,y_r)\}$ is called a $k$-signed $r$-set on
$[n]$ if $x_1,\dots,x_r$ are distinct elements of $[n]$ and
$y_1\dots,y_r\in[k]$. We say a $t$-intersecting family consisting of $k$-signed
$r$-sets on $[n]$ is trivial if each member of this family contains a fixed
$k$-signed $t$-set. In this paper, we determine the structure of large maximal
non-trivial $t$-intersecting families. In particular, we characterize the
non-trivial $t$-intersecting families with maximum size for $t\ge2$, extending
a Hilton-Milner-type result for signed sets given by Borg.
