  Ahern and Rudin have given an explicit construction of a totally real
embedding of $S^3$ in $\mathbb{C}^3$. As a generalization of their example, we
give an explicit example of a CR regular embedding of $S^{4n-1}$ in
$\mathbb{C}^{2n+1}$. Consequently, we show that the odd dimensional sphere
$S^{2m-1}$ with $m>1$ admits a CR regular embedding in $\mathbb{C}^{m+1}$ if
and only if $m$ is even.
