We performed calculations of nuclear systems composed solely of Λ* hyperons, aiming at exploring the possibility of existence of absolutely stable Λ* matter. We considered Λ* interaction strengths compatible with the Λ*Λ* binding energy BΛ*Λ* given by the ¯¯¯¯KN interaction model by Yamazaki and Akaishi. We found that the binding energy per Λ* saturates at values well below 100 MeV for mass number A ≥ 120. The Λ* matter is thus highly unstable against strong interaction decay.