  In our previous paper, we classified all $r$-uniform hypergraphs with
spectral radius at most $(r-1)!\sqrt[r]{4}$, which directly generalizes Smith's
theorem for the graph case $r=2$. It is nature to ask the structures of the
hypergraphs with spectral radius slightly beyond $(r-1)!\sqrt[r]{4}$. For
$r=2$, the graphs with spectral radius at most $\sqrt{2+\sqrt{5}}$ are
classified by [{\em Brouwer-Neumaier, Linear Algebra Appl., 1989}]. Here we
consider the $r$-uniform hypergraphs $H$ with spectral radius at most
$(r-1)!\sqrt[r]{2+\sqrt{5}}$. We show that $H$ must have a quipus-structure,
which is similar to the graphs with spectral radius at most
$\frac{3}{2}\sqrt{2}$ [{\em Woo-Neumaier, Graphs Combin., 2007}].
