The atomic and electronic structures of the (100) and (001) surfaces of the Al 5 Co 2 complex metallic alloy are studied by ab initio calculations. The relative stability of the possible surface planes built from bulk truncation is calculated and the influence of the atomic surface density, the interlayer spacing and the surface chemical composition on the plane selection is discussed. In addition, we show that the simulated images of scanning tunneling microscopy for each possible termination present a specific signature that appears to be sufficient to experimentally identify the surface plane.