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 < 1 (1) over bar1 > and < 1 (1) over bar2 > 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.