Hard X-ray focusing observation is important to reveal non-thermal emission mechanism and origin in active galaxies and clusters of galaxies. We have carried out the hard X-ray observation throughout the ¥infocus program, which is an international balloon-borne experiment in collaboration with NASA/GSFC and Nagoya University. The telescope is conical approximation of Wolter-I optics with 8 m focal length and 40 cm diameter. It consists of 255 nested thin (0.17 mm thickness) reflectors with incidence angles of 0.10° to 0.36°. Reflectors are coated with depth-graded platinum-carbon (Pt/C) multilayers, so-called supermirrors, with periodic length of 2.6 to 13 nm and bi-layer number of 28 to 79, depending on incidence angles. We are now continuously fabricating advanced next hard X-ray telescope for the second ¥infocus flight in 2004. Compared with the first telescope, the following improvements have been made on the second one. Supermirror reflectors have wider sensitivity in energy band of 20-60 keV adopting optimum supermirror design for balloon observation, and smaller interfacial roughness owing to complete replication technique. For upgrading of the image quality, we then adopted stiffer reflector substrate, selected replication mandrel with better shape, and the modified telescope housing with higher alignment accuracy for reflectors. The performance of the new hard X-ray telescope was measured in X-ray beamline facility in ISAS/JAXA and synchrotron radiation facility SPring-8. The effective area and image quality are obtained to be 45 cm2 at 30 keV and 23 cm2 at 40 keV, and 2.5 arcmin in half power diameter, respectively. In this paper we report our development of the upgraded hard X-ray telescope for the second balloon flight experiment.