Association analysis using the mining of positive and negative association rules (PNARs) has so far been mainly based on mining rules of forms A⇒B, A⇒ℸB, ℸA⇒B, and ℸA⇒ℸB. These are called narrow PNARs (NPNARs). Most existing algorithms for mining NPNARs usually exploit the upward closure property of negative itemsets, while few exploit the downward closure property. NPNARs mined by algorithms built under the first approach are inconsistent with human thinking and unsuitable for explaining association analysis. NPNARs mined by algorithms under the second approach are consistent with human thinking, but generally, they are just positive association rules or negative dependency relationships and are not intuitively described as the NPNARs above. Thus, they are confusing and difficult to interpret. So far, no algorithm built under both approaches has found all valid NPNARs. This work proposes an algorithm based solely on (positive) items in transaction databases under the second approach to mine NPNARs. The algorithm is developed based on equivalence classes and the support-confidence framework. Two phases of the association rule mining process are executed concurrently. The algorithm is sound and complete. Its computational complexity is also estimated. The experiment shows the application prospect of the proposed algorithm in the association analysis of co-occurrence and non-co-occurrence events.