  In the theory of partially-ordered sets, the two-dimensional Boolean lattice
is known as the diamond. In this paper, we show that, if $\mathcal{F}$ is a
family in the $n$-dimensional Boolean lattice that has no diamond as a
subposet, then $|\mathcal{F}|\leq 2.206653{n\choose \lfloor n/2\rfloor}$,
improving a bound by the authors and Michael Young.
