Cohort normalization is a method for normalizing the scores in speaker verification in order to reduce undesirable variation arising from acoustically mismatched conditions. A particular form of cohort normalization, unconstrained cohort normalization (UCN) is addressed in this study. The UCN method has been shown to give excellent results but its major drawback is the huge computational load arising from the search of the cohort speakers. In this paper, we propose a fast cohort search algorithm, that quantizes the test vector sequence and uses the quantized data for both impostor and claimant scoring. Results on the NIST-1999 corpus show a speed-up factor of 23:1 compared to full search. Furthermore, the equal error rates are decreased from those of the full search.