We investigate the characteristics of the surface mode formed at the single interface between dual singly negative medium layers. It is shown that the interface can support a mode which has polarization degeneracy and a vanishing propagation constant. That is, this surface mode is a polarization-independent one that does not propagate at all through the interface. The corresponding electric and magnetic field distributions become static along the longitudinal (guiding) direction (but not along the transverse direction) resulting in the formation of transverse-electric/longitudinalmagnetic or transverse-magnetic/longitudinal-electric modes.