  We complete the study of the topological period-index problem over 8
dimensional finite CW complexes started in a preceding paper. More precisely,
we determine the sharp upper bound of the index of a topological Brauer class
$\alpha\in H^3(X;\mathbb{Z})$, where $X$ is of the homotopy type of an 8
dimensional finite CW complex and the period of $\alpha$ is divisible by 4.
