We show that in a superconductor where two or more bands cross the Fer
mi level it is possible, in the framework of the conventional (s wave)
BCS theory, that the sign of the superconducting gap is different on
the different sheets of the Fermi surface. At least one of two conditi
ons has to be satisfied: (1) The interband pairing interaction is weak
er than the Coulomb pseudopotential, while the intraband one is strong
er, or (2) there is strong interband scattering by magnetic impurities
. In the case of YBa2Cu3O7 we shall argue that the first condition is
possibly satisfied, and the second one very likely satisfied. In many
aspects such a sign-reversal s wave superconductor is similar to a d w
ave superconductor, and thus demands revising recent experiments aimed
to distinguish between the s and d wave superconductivity in this com
pound.