  In 1984, Wilson proved the Erd\H{o}s-Ko-Rado theorem for $t$-intersecting
families of $k$-subsets of an $n$-set: he showed that if $n\ge(t+1)(k-t+1)$ and
$\mathcal{F}$ is a family of $k$-subsets of an $n$-set such that any two
members of $\mathcal{F}$ have at least $t$ elements in common, then
$|\mathcal{F}|\le\binom{n-t}{k-t}$. His proof made essential use of a matrix
whose origin is not obvious. In this paper we show that this matrix can be
derived, in a sense, as a projection of $t$-$(n,k,1)$ design.
