Redundant relations refer to explicit relations which can also be deducted implicitly. Although there exist several ontology redundancy elimination methods, they all do not take equivalent relations into consideration. Actually, real ontologies usually contain equivalent relations; their redundancies cannot be completely detected by existing algorithms. Aiming at solving this problem, this paper proposes a super-node based ontology redundancy elimination algorithm. The algorithm consists of super-node transformation and transitive redundancy elimination. During the super-node transformation process, nodes equivalent to each other are transferred into a super-node. Then by deleting the overlapped edges, redundancies relating to equivalent relations are eliminated. During the transitive redundancy elimination process, redundant relations are eliminated by comparing concept nodes' direct and indirect neighbors. Most notably, we proposed a theorem to validate real ontology's irredundancy. Our algorithm outperforms others on both real ontologies and synthetic dynamic ontologies.