An experimental demonstration of a wide-range narrowband multilayer mirror for selecting a single-order high-harmonic (HH) beam from multiple-order harmonics in the photon energy range between 40 eV and 70 eV was carried out. This extreme ultraviolet (XUV) mirror, based on a pair of Zr and Al0.7Si0.3 multilayers, has a reflectivity of 20-35% and contrast of more than 7 with respect to neighboring HHs at angles of incidence from 10 to 56.9 degrees, assuming HHs pumped at 1.55 eV. Thus, specific single-order harmonic beams can be arbitrarily selected from multiple-order harmonics in this photo energy range. In addition, the dispersion for input pulses of the order of 1 fs is negligible. This simple-to-align optical component is useful for the many various applications in physics, chemistry and biology that use ultrafast monochromatic HH beams.