A secluded supersonic SAW is known to exist in an isolated direction o
n the (001) surface of certain cubic crystals. This wave consists of t
wo evanescent partial wave components and is not polarized in a symmet
ry plane. Calculations are reported on this mode, using germanium as a
n example, and it is found that this wave continues to exist for some
surface orientations different from (001). A one dimensional family of
nonsymmetrical supersonic SAW geometries is identified and it is foun
d to be joined to the family of supersonic SAW polarized in the (1 $($
) over bar$$ 10) symmetry plane.