Although the full structure of the unit group of an integral group is not known, one can give for a lot of groups a finite set of generators for a subgroup of finite index in the unit group. As mentioned above, the obstruction is given by exceptional components in the Wedderburn decomposition of the rational group algebra. To overcome this problem I introduced unitary units. With these units it is possible to give a subgroup of finite index in the unit group of the integral group ring of all groups of order 16. In this article we extended this result to a special class of groups.