  We discuss the cyclic Wilson loop, i.e. a rectangular Wilson loop that spans
the entire compactified time axis in the imaginary time formalism. The result
of a perturbative calculation at $O(\alpha_s^2)$ is given, with the main focus
on the ultraviolet divergences of this operator. Based on a general analysis of
divergences in loop diagrams, we find that, unlike usual Wilson loops, the
cyclic loop does not have cusp divergences but intersection divergences, where
the intersections arise due to the periodic boundary conditions. As a result,
the cyclic Wilson loop itself is not multiplicatively renormalizable, but the
difference between it and the correlator of two Polyakov loops is.
