Let $k\ge 4$. If $\mathcal{F}$ is a family of subsets of $\{1,\dots ,n\}$ with $|A|=k$ for all $A\in \mathcal{F}$ and $|\mathcal{F}|>\left(\genfrac{}{}{0ex}{}{n-2}{k-2}\right)$ then there are $A,B\in \mathcal{F}$ such that $|A\cap B|=1$.