The electronic structure of a semi-infinite superlattice (SL) with a c
omplex basis consisting of two identical wells coupled via two differe
nt barriers is investigated. The possibility of the surface state exis
tence for a periodic termination of the SL potential (i.e., without pe
rturbing the SL potential at the surface) is shown for such a two-barr
ier basis, in contrast to the conventional one of single well and barr
ier. This main conclusion is based on analytical considerations, howev
er, some numerical results for the GaAs/AlAs SL are also presented.