Ontologies, often defined as an explicit specification of conceptualization, are necessary for knowledge representation and knowledge exchange. Usually this means that ontology describes concepts and relations that exist in a domain. To enable knowledge exchange, it is necessary to describe these concepts and relations in a better way than just ordering them in taxonomy. However, ontology design usually starts and stops with designing taxonomies. We present a method that is based on formal concept analysis, which is a theory of data analysis which identifies conceptual structures among data sets. This method allows for discovering necessity for new concepts and relations in an ontology, which leads to an ontology that has these entities described in a way suitable for knowledge exchange.