Given a set S of n points in the Euclidean plane, two-center problem is to find two congruent disks smallest radius whose union covers all S. Previously, Eppstein (SODA’97) gave randomized algorithm $$O(n\log ^2\!n)$$ expected time and Chan (CGTA’99) presented deterministic ^2\!n\log ^2\log n)$$ time. In this paper, we propose an algorithm, which improves Chan’s matches bound Eppstein. If conve...