Existing association-rule mining algorithms often rely on the support-based pruning strategy to prune its combinatorial search space. This strategy is not quite effective for data sets with skewed support distributions because they tend to generate many spurious patterns involving items from different support levels or miss potentially interesting low-support patterns. To overcome these problems, we propose the concept of hyperclique pattern, which uses an objective measure called h-confidence to identify strong affinity patterns. We also introduce the novel concept of cross-support property for eliminating patterns involving items with substantially different support levels. Our experimental results demonstrate the effectiveness of this method for finding patterns in dense data sets even at very low support thresholds, where most of the existing algorithms would break down. Finally, hyperclique patterns also show great promise for clustering items in high dimensional space.