  We performed calculations of nuclear systems composed solely of $\Lambda^*$
hyperons, aiming at exploring the possibility of existence of absolutely stable
$\Lambda^*$ matter. We considered $\Lambda^*$ interaction strengths compatible
with the $\Lambda^*\Lambda^*$ binding energy $B_{\Lambda^*\Lambda^*}$ given by
the $\bar{K}N$ interaction model by Yamazaki and Akaishi [1]. We found that the
binding energy per $\Lambda^*$ saturates at values well below 100 MeV for mass
number $A\geq120$. The $\Lambda^*$ matter is thus highly unstable against
strong interaction decay.
