Inheritance is the main theme of schema design for an object-oriented database. It contributes to good properties of modularity, reusability and incremental design. However, once and object-oriented database schema is inserted or deleted during the lifetime of a database, it is prone to lead to redundant inheritance (IS-A) relationships, which suffer from massive data redundancy and inconsistency. To ensure the consistency and nonredundancy of the OODB schema after every insertion or deletion, we propose a rapid detection method by mapping a class hierarchy to a transitive closure matrix in this paper. A faster algorithm for computing a transitive closure matrix with respect to a class hierarchy is presented to help to detect redundant inheritance. Its time complexity is O(k×n). Also, an algorithm to eliminate redundant inheritance is proposed.