  We classify stably/retract rational norm one tori in dimension $n-1$ for
$n=2^e$ $(e\geq 1)$ is a power of $2$ and $n=12, 14, 15$. Retract
non-rationality of norm one tori for primitive $G\leq S_{2p}$ where $p$ is a
prime number and for the five Mathieu groups $M_n\leq S_n$ $(n=11,12,22,23,24)$
is also given.
