For a finite group $G$, we introduce a multiplication on the $\QQ$-vector
space with basis $\scrS_{G\times G}$, the set of subgroups of $G\times G$. The
resulting $\QQ$-algebra $\Atilde$ can be considered as a ghost algebra for the
double Burnside ring $B(G,G)$ in the sense that the mark homomorphism from
$B(G,G)$ to $\Atilde$ is a ring homomorphism. Our approach interprets $\QQ
B(G,G)$ as an algebra $eAe$, where $A$ is a twisted monoid algebra and $e$ is
an idempotent in $A$.