The growth and magnetic domain structure of ultrathin Fe films epitaxially grown on face-centered cubic (fcc) Rh(001) is investigated by spin-polarized scanning tunneling microscopy (SP-STM) at low temperatures (T = 5.5K). Our results indicate that the cleaning procedure applied to the Rh(001) substrate plays an important role for the formation of a clean and well-ordered Fe film. The Fe monolayer exhibits an out-of-plane antiferromagnetic c(2 × 2) spin structure. Islands of the second Fe layer are found to be out-of-plane ferromagnetic. Coalescence of the double-layer islands results in the formation of larger domains, which extend over several hundred nanometers for a closed two layer film. Further increasing the Fe coverage leads to a reduction of the domain size and the formation of patterns that are reminiscent of stripe domains driven by the competition of surface/interface and shape anisotropy.