Transmission electron diffraction and reflection high-energy electron diffraction have been used to study thermal vibrations at the InSb(111)A-(2x2) surface. The surface In and Sb atoms show a large anisotropy in their vibrational amplitudes. In particular, contrary to common belief, the Debye temperature of surface In (Sb) atoms is larger than the corresponding bulk value in the directions normal (parallel) to the surface. We show that thermal vibrations in these directions are suppressed so as to maintain the sp(2)-type (p(3)-type) bonding character of surface In (Sb) atoms with their nearest neighbors.