High-quality single crystals are essentially needed for the investigation of the novel bulk properties of unconventional superconductors. The availability of such crystals grown by the floating-zone method has helped to unveil the unconventional superconductivity of the layered perovskite Sr2RuO4, which is considered as a strong candidate of a topological spin-triplet superconductor. Yet, recent progress of investigations urges further efforts to obtain ultimately high-quality crystalline samples. In this paper, we focus on the method of preparation of feed rods for the floating-zone melting and report on the improvements of the crystal growth. We present details of the improved methods used to obtain crystals with superconducting transition temperatures Tc that are consistently as high as 1.4 K, as well as the properties of these crystals.