Attribute exploration in FCA is proposed by Baader etc. in the past decade and it is an effective tool applying to description logics to construct ontology on Semantic Web. The authors firstly introduce attribute exploration algorithm, then investigate different cases in which the redundant computation may occur. As new results, the improved attribute exploration algorithm is proposed in terms of relevancy. We also give the proof of the completeness of the improved algorithm, and show how the proposed algorithm avoids redundancy and simplifies computation in some certain cases. We finally present the method to construct an ontology based on attribute exploration algorithm(AEOCM) on the open formal context, and specify the implement-tation procedure of this method in terms of instantiation.