High-utility itemset mining (HUIM) is an emerging data mining topic. It aims to find the high-utility itemsets by considering both the internal (i.e., quantity) and external (i.e., profit) utilities of items. High-average-utility itemset mining (HAUIM) is an extension of the HUIM, which provides a more fair measurement named average-utility, by taking into account the length of itemsets in addition to their utilities. In the literature, several algorithms have been introduced for mining high-average-utility itemsets (HAUIs). However, these algorithms assume that databases contain only positive utilities. For some real-world applications, on the other hand, databases may also contain negative utilities. In such databases, the proposed algorithms for HAUIM may not discover the complete set of HAUIs since they are designed for only positive utilities. In this study, to discover the correct and complete set of HAUIs with both positive and negative utilities, an algorithm named MHAUIPNU (mining high-average-utility itemsets with positive and negative utilities) is proposed. MHAUIPNU introduces an upper bound model, three pruning strategies, and a data structure. Experimental results show that MHAUIPNU is very efficient in reducing the size of the search space and thus in mining HAUIs with negative utilities.