  $(\tau^+\tau^-)_b$ is an atom of simple hydrogenlike structure similar to
positronium $(e^+e^-)_b$ and $(\mu^+\mu^-)_b$. In this paper energy levels and
decay widths of different decay channels of $(\tau^+\tau^-)_b$ are given. Cross
section of production of this atomic system in $e^+e^-$ annihilation taking
into account radiative corrections is calculated. According to our estimates
886 $(\tau^+\tau^-)_b$ atoms may be produced at BEPCII and 29
$(\tau^+\tau^-)_b$ atoms are produced at VEPP-4M under the present experimental
conditions.
