  We study the decay behaviors of the fully-bottom tetraquark states within the
diquark-antidiquark picture, and calculate their relative branching ratios
through the Fierz rearrangement. Our results suggest that the $C=+$ states can
be searched for in the $\mu^+ \mu^- \Upsilon(1S)$ and $\mu^+ \mu^-
\Upsilon(2S)$ channels with the relative branching ratio $\mathcal{B}(X \to
\mu\mu \Upsilon(2S)) / \mathcal{B}(X \to \mu \mu \Upsilon(1S)) \approx 0.4$.
Our results also suggest that the $C=-$ states can be searched for in the
$\mu^+ \mu^- \eta_b(1S)$ and $\mu^+ \mu^- \eta_b(2S)$ channels with the similar
relative branching ratio $\mathcal{B}(X \to \mu\mu \eta_b(2S)) / \mathcal{B}(X
\to \mu \mu \eta_b(1S)) \approx 0.4$. We also reanalysis the fully-charm
tetraquark states, and study the $X(6900)$ decay into the $J/\psi \psi(2S)$
channel to obtain the relative branching ratio $\mathcal{B}(X \to J/\psi
\psi(2S)) / \mathcal{B}(X \to J/\psi J/\psi) \approx 0.1$.
