  A $(k,\ell )$ partial partition of an $n$-element set is a collection of
$\ell $ pairwise disjoint $k$-element subsets. It is proved that, if $n$ is
large enough, one can find $\left\lfloor {n\choose k}/{\ell}\right\rfloor$ such
partial partitions in such a way that if $A_1$ and $A_2$ are distinct classes
in one of the partial partitions, $B_1$ and $B_2$ are distinct classes in
another one, then one of the intersections $A_1\cap B_1, A_2\cap B_2$ has size
at most ${k\over 2}$.
