  An important issue in classifying the rational $3$-tangle is how to know
whether or not the given tangle is the trivial rational 3-tangle called
$\infty$-tangle. The author\cite{1} provided a certain algorithm to detect the
$\infty$-tangle. In this paper, we give a much simpler method to detect the
$\infty$-tangle by using the $\textit{bridge arc replacement}$. We hope that
this method can help prove many application problems such as the classification
of $3$-bridge knots.
