  Let $G$ be a locally compact group, and let $WAP(G)$ denote the space of
weakly almost periodic functions on $G$. We show that, if $G$ is a
$[SIN]$-group, but not compact, then the dual Banach algebra $WAP(G)^\ast$ does
not have a normal, virtual diagonal. Consequently, whenever $G$ is an amenable,
non-compact $[SIN]$-group, $WAP(G)^\ast$ is an example of a Connes-amenable,
dual Banach algebra without a normal,virtual diagonal.
