Identifying the discriminative characteristic of a query is important for image retrieval. For retrieval without human interaction, such characteristic is usually obtained by average query expansion (AQE) or its discriminative variant (DQE) learned from pseudo-examples online, among others. In this paper, we propose a new query expansion method to further improve the above ones. The key idea is to learn a "unique'' discriminative characteristic for each database image, in an offline manner. During retrieval, the characteristic of a query is obtained by aggregating the unique characteristics of the query-relevant images collected from an initial retrieval result. Compared with AQE which works in the original feature space, our method works in the space of the unique characteristics of database images, significantly enhancing the discriminative power of the characteristic identified for a query. Compared with DQE, our method needs neither pseudo-labeled negatives nor the online learning process, leading to more efficient retrieval and even better performance. The experimental study conducted on seven benchmark datasets verifies the considerable improvement achieved by the proposed method, and also demonstrates its application to the state-of-the-art diffusion-based image retrieval.