Abstract
We characterise number fields without a unit primitive element, and we exhibit some families of such fields with low degree. Also, we prove that a noncyclotomic totally complex number field K, with degree 2d where d is odd, and having a unit primitive element, can be generated by a reciprocal integer if and only if K is not CM and the Galois group of the normal closure of K is contained in the hyperoctahedral group B-d.