  We search for the decays of the $B^0$ meson into $e^+e^-$, $\mu^+\mu^-$
$e^{\pm}\mu^{\mp}$ pairs in a sample of $9.7\times 10^6$ $B{\bar B}$ pairs
recorded by CLEO detector. No signal is found, and the following upper limits
on the corresponding branching fractions are established: $<8.3\times 10^{-7}$,
$<6.1\times 10^{-7}$, $< 15\times 10^{-7}$ at 90% confidence level. A new lower
limit on the Pati-Salam leptoquark mass $M_{LQ}>27$ TeV is established at 90%
confidence level.
