Let \(G\) be a finite group and let \(\mathbb{Z} G\) be the group ring of \(G\) over \(\mathbb{Z}\). The question of determining a subgroup of finite index in the group of units of \(\mathbb{Z} G\) recently got answers for many groups. The method is to produce a class of ‘generic units’ which generate a subgroup of finite index in the projection onto the Wedderburn components. For abelian groups \(G\), the ‘Bass cyclic units’ generate a subgroup of finite index in the unit group of \(\mathbb{Z} G\), for more general groups the ‘bicyclic units’ \({\mathcal B}_2\) and \({\mathcal B}_2'\) together with the Bass cyclic units generate a subgroup of finite index in the unit group of \(\mathbb{Z} G\). The authors introduce a new type of generic units \({\mathcal B}_3\) which, together with the Bass cyclic units and the bicyclic units, generate a subgroup of finite index in the unit group of \(\mathbb{Z} G\) for a class of finite nilpotent groups \(G\) which extends the cases already treated by J. Ritter and the second author [Trans. Am. Math. Soc. 324, 603-621 (1991; Zbl 0723.16016)] as well as E. Jespers and G. Leal [Manuscr. Math. 78, 303-315 (1993; Zbl 0802.16025) and Commun. Algebra 23, 623-628 (1995; Zbl 0821.16036)].