Alloys of Co1−xMnx were grown epitaxially on GaAs(001) substrates. Unlike bulk alloys, nanometer-thick layers are found to have a much higher Curie temperature and are ferromagnetic over a wider range of Mn concentration, extending from x=0 to 0.8. The enhanced ferromagnetism is attributed to the strained tetragonal lattice which is in registration with the GaAs(001) lattice. This demonstrates the utility of tailoring magnetic properties with strain-layer epitaxy.