  We give an estimate of the $C$-even $B^0 \bar{B^0}$ background coming from
the radiative decay $\Upsilon(4S)\to B^0\bar B^0\gamma$ at $B$-factories. Our
result $B(\Upsilon(4S)\to B^0\bar B^0\gamma) \simeq 3 \times 10^{-9}$ shows
that such background could be safely neglected in the analyses of $CP$
violating effects.
