We study the real cyclic sextic fields generated by a root w of
(
X
−
1
)
6
−
(
t
2
+
108
)
(
X
2
+
X
)
2
{(X - 1)^6} - ({t^2} + 108){({X^2} + X)^2}
,
t
∈
Z
−
{
0
,
±
6
,
±
26
}
t \in {\mathbf {Z}} - \{ 0, \pm 6, \pm 26\}
. We show that, when
t
2
+
108
{t^2} + 108
is square-free (except for powers of 2 and 3), and
t
≠
0
t \ne 0
,
±
10
\pm 10
,
±
54
\pm 54
, then w is a generator of the module of relative units. The details of the proofs are given in [3].