Recently, some researchers have developed incremental and online mining approaches to maintain association rules without having to re-process the entire database whenever the database is updated or user specified thresholds are changed. However, they usually can not flexibly obtain association rules or patterns from portions of data, consider problems with different aspects, or provide online decision support for users. We earlier developed an online mining approach for generation of association rules under multidimensional consideration. The multidimensional online mining approach may, however, get loose upper-bound support of candidate itemsets and thus cause excessive I/O and computation costs. In this paper, we attempt to apply the concept of a negative border to enlarge the mining information in the multidimensional pattern relation to help get tighter upper-bound, and thus reduce the number of candidate itemsets to consider. Based on the extended multidimensional pattern relation, a corresponding online mining approach called Negative-Border Online Mining (NOM) is proposed to efficiently and effectively utilize the information of negative itemset in the negative border. Experiments for heterogeneous datasets are also performed to show the effectiveness of the proposed approach.