In this paper, the current research progresses of ontology reuse is reviewed and the issue that current ontology reuse algorithms can merely be applied to a single independent ontology is addressed. Focusing on the modular ontologies with ε-Connections language, the IK_MO (integrity of knowledge about the module in an ontology) is presented based on the theory of conservative extension. The related properties of IK_MO are proved. Further, an algorithm for the ontology reuse with the conservative extension ERMMO (extracting reused modules from modular ontologies) is provided. The features and conditions of two sub-algorithms of ERMMO are discussed. Lastly, the feasibility and soundness of ERMMO are analyzed and verified. ERMMO is a generalization of the current reuse algorithms based on conservative extension theory, and can be served as the guidelines for reuse of modular ontologies.