  A new method is proposed to search for the double beauty tetraquark
$bb\bar{u}\bar{d}$ with a mass below the $BB$ threshold. The
$b\bar{d}-\bar{b}d$ mixing can result in evolution of the tetraquark content to
$b\bar{b}\bar{u}d$ with the following strong decay into the
$\Upsilon$(1S)$\pi^-$ and $\Upsilon$(2S)$\pi^-$ final states in a secondary
vertex displaced from the primary $pp$ collision vertex. This experimental
signature is clean, has a high selection efficiency and can be well separated
from backgrounds. Experimental signatures for searches for other double heavy
tetraquarks are also discussed, suggesting the possibility of the $b\bar{d}$ or
$b\bar{s}$ mixing.
