Inter-transaction pattern and rule mining has been the subject of active research and has potential application in many areas. All the previous inter-transaction rule mining studies proposed generating a full set of inter-transaction rules (i.e., all frequent and confident rules) from a full set of inter-transaction patterns (i.e., all frequent patterns). However, generating a full set inter-transaction rules can be very expensive. In this paper, to resolve the explosive growth of inter-transaction rules, we propose a new research of mining non-redundant inter-transaction rules. We investigate and characterize non-r edundant inter-transaction rules, study the quality inter-transaction rule sets with respect to completeness and tightness. We develop an algorithm named NRITR-Miner to mine the non-redundant inter-transaction rules efficiently and an algorithm named ITR-Miner to mine the full-set of inter-transaction rules for comparing purpose. We demonstrate via experiments that the proposed algorithm is efficient and scalable, and outperform the compared algorithm in all cases.