The function fα(z) = ({(1 + z)/(1 - z)}α - 1)/(2α) with a complex constant α ≠ 0 is not univalent in the disk U = {|z| &lt
1} if and only if α is not in the union A of the closed disks {|z + 1| ≤ 1} and {|z - 1| ≤ 1}. By making use of a geometric quantity we can describe how fα "continuously tends to be" univalent in the whole U as α tends to each boundary point of A from outside.