Summary: We describe an $O(\min(m,n^{3/2})m^{1/2})$-time algorithm for finding maximum flows in undirected networks with unit capacities and no parallel edges. This improves upon the previous bound of Karzanov and Even and Tarjan when $m = ω(n^{3/2})$, and upon a randomized bound of Karger when $v = Ω(n^{7/4}/m^{1/2})$.