The groupoid identity $x(xy)=y$ appears in definitions of several classes of groupoids, such as Steiner loops (which are closely related to Steiner triple systems) [9,10], orthogonality in quasigroups [4] and others [12,2]. We have considered in [8] several varieties of groupoids that include this identity among their defining identities, and here we consider the variety ${\mathcal V}$ of semigroups defined by the same identity. The main results are: the decomposition of a ${\mathcal V}$ semigroup as a direct product of a Boolean group and a left unit semigroup; decomposition of the variety ${\mathcal V}$ as a direct product of the variety of Boolean groups and the variety of left unit semigroups; constructions of free objects in ${\mathcal V}$ and the solution of the word problem in ${\mathcal V}$.