A palmprint identification system recognizes a query palmprint image by searching for its nearest neighbor from among all the templates in a database. When applied on a large-scale identification system, it is often necessary to speed up the nearest-neighbor searching process. We use competitive code, which has very fast feature extraction and matching speed, for palmprint identification. To speed up the identification process, we extend the cover tree method and propose to use a set of cover trees to facilitate the fast and accurate nearest-neighbor searching. We can use the cover tree method because, as we show, the angular distance used in competitive code can be decomposed into a set of metrics. Using the Hong Kong PolyU palmprint database (version 2) and a large-scale palmprint database, our experimental results show that the proposed method searches for nearest neighbors faster than brute force searching.