  A binary fluid mixture of non-additive hard spheres characterized by a size
ratio $\gamma=\sigma_2/\sigma_1<1$ and a non-additivity parameter
$\Delta=2\sigma_{12}/(\sigma_1+\sigma_2)-1$ is considered in infinitely many
dimensions. From the equation of state in the second virial approximation
(which is exact in the limit $d\to\infty$) a demixing transition with a
critical consolute point at a packing fraction scaling as $\eta\sim d 2^{-d}$
is found, even for slightly negative non-additivity, if
$\Delta>-{1/8}(\ln\gamma)^2$. Arguments concerning the stability of the
demixing with respect to freezing are provided.
