  In this work, we assume that the observed state $\Xi(1620)$ is a $s$-wave
$\Lambda\bar{K}$ or $\Sigma\bar{K}$ bound state. Based on this molecule
picture, we establish the Bethe-Salpeter equations for $\Xi(1620)$ in the
ladder and instantaneous approximations. We solve the Bethe-Salpeter equations
for the $\Lambda\bar{K}$ and $\Sigma\bar{K}$ systems numerically and find that
the $\Xi(1620)$ can be explained as $\Lambda\bar{K}$ and $\Sigma\bar{K}$ bound
states with $J^P=1/2^-$, respectively. Then we calculate the decay widths of
$\Xi(1620)\rightarrow\Xi\pi$ in these two different molecule pictures systems,
respectively.
