  Let $k$ be a field, and let $L$ be an \'etale k-algebra of finite rank. If
$a$ is a nonzero element in $k$, let $X_a$ be the affine variety defined by the
norm equation $N_{L/k}(x) = a$. Assuming that $L$ has at least one factor that
is a cyclic field extension of $k$, we give a combinatorial description of the
unramified Brauer group of $X_a$.
