We propose to exploit the angular distribution of the positrons emitted in the reaction <(nu)over bar>(e) + p --> n + e(+) to extract a possible antineutrino signal from the Superkamiokande background. From the statistics collected in just 101.9 days one obtains a model independent upper bound on the antineutrino flux Phi(nu)- (E(nu)-> 8.3 MeV) < 9 . 10(4) cm(-2) s(-1) at the 95% C.L. By assuming the same energy spectrum as for the (8)B neutrinos, the 95% C.L. bound is Phi(nu)- (E(nu)-> 8.3 MeV) < 6 . 10(4) cm(-2) s(-1). Within three years of data taking, the sensitivity to nu(e) --> <(nu)over bar>(e) transition probability will reach the 1% level, thus providing a stringent test of hybrid oscillation models. (C) 1997 Elsevier Science B.V.