This study extends conventional fingerprint recognition from a supervised to an unsupervised framework. Instead of enrolling fingerprints from known persons to identify unknown fingerprints, our aim is to partition a collection of unknown fingerprints into clusters, so that each cluster consists of fingerprints from the same finger and the number of generated clusters equals the number of distinct fingers involved in the collection. Such an unsupervised framework is helpful to handle the situation where a collection of captured fingerprints are not from the enrolled people. The task of fingerprint clustering is formulated as a problem of minimizing the clustering errors characterized by the Rand index. We estimate the Rand index by computing the similarities between fingerprints and then apply a genetic algorithm to minimize the Rand index. Experiments conducted using the FVC2002 database show that the proposed fingerprint clustering method outperforms an intuitive method based on hierarchical agglomerative clustering. The experiments also show that the number of clusters determined by our system is close to the true number of distinct fingers involved in the collection.