In a regular semigroup \(S\), an inverse subsemigroup \(S^\circ\) of \(S\) is called an inverse transversal of \(S\) if \(S^\circ\) contains a unique inverse \(x^\circ\) of each element \(x\) of \(S\). The subject of this paper is the class of biordered sets of regular semigroups with inverse transversals, known throughout as IT-biordered sets. For example, the fundamental regular semigroup \(T_E\) is described when \(E\) is an IT-biordered set. A construction is presented of an IT-biordered set by a so-called left regular IT-biordered set and a right regular IT-biordered set.