Nowadays, ontologies as basic information technology are constructed in various domains such as medical information, engineering design, automated vehicles, and environmental issues. The quality of these ontologies, which serve as the base of domain knowledge, is a critical issue in determining the performance of application systems. Therefore, a number of guidelines for ontology construction have been proposed so far, and some ontology construction and refinement methods have implemented in support systems. In this study, we propose a new method that focuses on sibling relations in is-a (subclassOf) hierarchy in addition to super-sub relations. Then, we implement it into a new ontology-construction support system. In our previous study, we developed a comparison method that focused only on super-sub relations. Our new refinement method ensures not local but comprehensive is-a hierarchy. Evaluation was performed as follows. On five ontologies, five beginners and twelve experts of ontology construction used the new system to test the applicability of suggestion from the system. We evaluated 108 refinement points that were randomly extracted from the suggestions. As a result, 105 points out of 108 points (97%) were judged to be refined by beginners, and 88 points out of 108 points (81%) were judged to be refined by experts. Thus, this test proved the effectiveness and usefulness of our proposed method.