We consider the propagation of plasma modes in superconducting films b
ound by a high-dielectric-constant medium and predict a mode that corr
esponds to the anti-symmetric coupling of the two surface plasmons. We
show that anisotropy plays a determinant role in lowering this mode's
frequency range, bringing it to the realm of possible experimental ob
servation for the high-T-c superconductors. Theoretical predictions fo
r the maximal and minimum him thickness, where this mode can be found
below the plasma frequency along the c-axis, are also made here.