In applications of solar physics, extreme ultraviolet imaging of solar corona by selecting the He-II (l530.4 nm) emission line requires high reflectivity multilayer mirrors. Some material combinations were studied to design the mirrors working at a wavelength of 30.4 nm, including SiC/Mg, B4C/Mg, C/Mg, C/Al, Mo/Si, B4C/Si, SiC/Si, C/Si, and Sc/Si. Based on optimization of the largest reflectivity and the narrowest width for the multilayer mirror, a SiC/Mg material combination was selected as the mirror and fabricated by a magnetron sputtering system. The layer thicknesses of the SiC/Mg multilayer were measured by an X-ray diffractometer. Reflectivities were then measured on beamline U27 at the National Synchrotron Radiation Laboratory (NSRL) in Hefei, China. At a wavelength of 30.4 nm, the measured reflectivity is as high as 38.0%. Furthermore, a series of annealing experiments were performed to investigate the thermal stability of the SiC/Mg multilayer.