By making use of McAlister’s P-theorem [4] O’Carroll proved in [5] that every E-unitary inverse semigroup can be embedded into a semidirect product of a semilattice by a group. Recently an alternative proof of this result was published by Wilkinson [10]. In this paper we generalize this theorem by proving that every E-unitaryR-unipotent semigroup S can be embedded into a semidirect product of a band B by a group where B belongs to the variety of bands generated by the band of idempotents of S.