An abnormal dependence of the rate of amyloid formation on protein concentration has been recently observed by Meisl et al. for Aβ40 peptides associated with Alzheimer's disease. To explain this effect, Meisl et al. proposed a novel mechanism of fibril growth: the fibril-catalyzed initiation of fibril formation. In this paper we offer an alternative explanation of the observed anomalous kinetics: formation of metastable oligomers competing with fibril formation by decreasing the concentration of the fibril-forming free monomers. Here we show that the oligomer sizes resulting from the anomalous dependence of the fibril growth rate on protein concentration are close to the sizes of oligomers observed by electron microscopy.