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The structural and magnetic properties of epitaxial Fe(001) ultrathin films (0.9-17 nm) deposited by molecular beam epitaxy at room temperature on Al0.48In0.52As(001) layers have been studied by magneto-optical Kerr effect and X-ray diffraction (XRD) experiments. Fe grows in a body centered cubic (bcc) structure with epitaxial relationship Fe(001)<100>//Al0.48In0.52As(001)<100>. XRD measurements demonstrate a pseudomorphous growth of Fe films up to 4.4 nm and then the layers progressively relax with the Fe thickness. All Fe films are ferromagnetic at room temperature and show an in-plane magnetization with a fourfold anisotropy (with <100> as easy axes) superimposed to an uniaxial anisotropy (with  as easy axis). The uniaxial contribution finds its origin essentially in the interface anisotropy, as it is the case for the Fe/GaAs(001) system. We found that in the pseudomorphous range of the Fe films, the volume fourfold anisotropy constant is 60% larger than the bulk Fe value. We attribute this increase to the in-plane biaxial tensile strain in the films through magneto-elastic coupling effects.