Direct Measurement of the Branching Fraction of \boldmath{$\Upsilon(4S) \rightarrow B^0 \bar {B}^{0}$}

We report the first direct measurement of the branching fraction of $\Upsilon(4S) \rightarrow B^0 \bar {B}^{0}$ carried out with a data sample of 82~fb$^{-1}$ collected at the $\Upsilon(4S)$ resonance with the BaBar detector at the PEP-II asymmetric-energy $B$ Factory at SLAC. Our result is obtained with a double-tag technique and does not depend on branching fractions of the $\bar {B}^{0}$ and the $D^{*+}$ decays, on the simulated reconstruction efficiency, on the ratio of the charged and neutral $B$ meson lifetimes, or on the assumption of isospin symmetry.