The results of the low-temperature ultrahigh-energy-resolution photoemission studies of a single-grain icosahedral alloy Al70Pd21.5Mn8.5 have been presented. The existence of the theoretically predicted pseudogap in the density of states at the Fermi energy has been confirmed. No evidence of the theoretically predicted spikiness of the density of states could be observed. It has been suggested that the failure to detect the predicted spikiness of the density of states in icosahedral quasicrystals is consistent with the results of Zijlstra and Janssen [Europhys. Lett. 52, 578 (2000)] who showed that the spikiness occurs only in lower-order periodic approximants to icosahedral quasicrystals, but does not survive in the quasiperiodic limit.