We have used the pseudo-tenfold surface of the orthorhombic Al(13)Co(4) crystal as a template for the adsorption of Cu thin films of various thicknesses deposited at different temperatures. This study has been carried out by means of low energy electron diffraction (LEED), scanning tunnelling microscopy (STM), x-ray photoelectron spectroscopy (XPS) and x-ray photoelectron diffraction (XPD). From 300 to 573 K, Cu adatoms grow pseudomorphically up to one monolayer. At 300 K, the β-Al(Cu, Co) phase appears for coverages greater than one monolayer. For higher temperature deposition, the β-Al(Cu, Co) phase further transforms into the γ-Al(4)Cu(9) phase. Both β and γ phases grow as two (110) domains rotated by 72° ± 1° from each other. Instead of following the substrate symmetry, it is the orientations of the bipentagonal motifs present on the clean Al(13)Co(4)(100) surface that dictate the growth orientation of these domains. The initial bulk composition and structural complexity of the substrate have a minor role in the formation of the γ-Al(4)Cu(9) phase as long as the amount of Al and the Cu film thickness reach a critical stoichiometry.