The elucidation of the local atomic structure of a pseudomorphic film of Cu deposited on the five-fold surface of i-Al₇₀Pd₂₁Mn₉using medium-energy ion scattering spectroscopy is reported. Monte Carlo calculations, using the VEGAS code, have been utilized to simulate the blocking of 100 keV He+ ions scattered from the overlayer. The coordinates of the Cu atoms in the overlayer derived from this procedure are consistent with a structure occurring in five rotational domains. Each domain consists of nanoscale strips of fcc Cu(100) with the ⟨110⟩ azimuth aligned along the five-fold directions of the quasicrystalline substrate. The strips are arranged according to a one-dimensional Fibonacci sequence with long and short widths related by the golden mean τ. Upon annealing the film transforms to an alloyed structure composed of five orientational domains of fcc material with the (110) axis perpendicular to the surface.