Simple group-theoretical arguments are used to demonstrate that in the
high temperature (chirally restored) phase of QCD with N-f massless f
lavours, all n-point correlation functions of quark bilinears are inva
riant under U(1)(A) transformations provided n < N-f. In particular th
is implies that the two-point correlation function in the eta' channel
is identical to that in the pion channel for N-f > 2. Unlike previous
work, this result does not depend on the topological properties of QC
D and can be formulated without explicit reference to functional integ
rals.