We search for the decay of the B-0 meson into a pair of leptons in the supp
ressed channels B-0-->e(+)e(-), B-0-->mu (+)mu (-) and in the lepton number
violating channel B-0-->e(+/-)mu (-/+) in a sample of 9.7 x 10(6) B(B) ove
r bar pairs recorded corded by CLEO detector. No signal is found, and the f
ollowing upper limits on the branching fractions are established: B(B-0-->e
(+)e(-))<8.3 x 10(-7), B(B-0-->mu (+)mu (-))<6.1 x 10(-7), B(B-0-->e(+/-)mu
(-/+))<15 x 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.