In this paper, an inherent relationship between MUPS and MIPS is obtained by defining covering relations of unsatisfiable concepts and developing the definition of R-MUPS of unsatisfiable concept. Then a proof is given that there exists at least one unsatisfiable concept whose R-MUPS is also a MIPS for every MIPS. Based on this conclusion, an R-MUPS algorithm based on the ordered label calculus is proposed. It applies depth-first traversal in merging branches to calculate R-MUPS, and also caches the concepts of covered at the same time to speed up the solving of MIPS to achieve ontology debugging. Through revealing the equivalence between concept expansion tree and R-MUPS algorithm, the correctness of R-MUPS algorithm is proved, and its complexity is further analyzed. Finally, a comprehensive test is performed using automatically generated ontology test sets, realistic ontology and its expansion ontology. The experimental results show that the solving of MIPS based on R-MUPS algorithm can efficiently and accurately complete the ontology debugging tasks.