The in-plane orientation of the magnetization vector M in bcc-like Fe(110) films grown on Cu(001) is determined by means of scanning electron microscopy with polarization analysis. For thicknesses of 2 nm, slightly above the fcc/bcc phase transition, it is found that M is oriented along the 110 directions of the Cu (001) substrate. Following the Pitsch orientational relationship these correspond to magnetically hard 111 and 112 axes of bulk iron. This finding is in strong contrast to the behavior reported for thicker films (above 3 nm) of bcc Fe/Cu(001), where the 100 directions of the substrate are preferred. The role of strain in the iron film is discussed, inferring that the presence of a shear strain is mandatory to explain the spin reorientation via the magnetoelastic contribution to the magnetic anisotropy energy.