A subclass of *inverse semigroups is in vestigated in this paper, namely, U*inverse semigroups. Besides, the paper gives that a semigroup is an U*inverse semigroups if and only if for any x∈S there exists a unique element x0∈H*1 such that x≤x0. Moreover, the paper proves that an U*inverse semigroups is F-Abundant semigroups if and only if, M=H*1，so that L*inverse semigroups and F-Abundant semigroups are connected.