The [PSI+] prion determinant of Saccharomyces cerevisiae causes nonsense suppressor phenotype due to a reduced function of the translation termination factor Sup35 (eRF3) polymerized into amyloid fibrils. Prion state of the Rnq1 protein, [PIN+], is required for the [PSI+] de novo generation but not propagation. Yeast [psi-] [PIN+] cells overproducing Sup35 can exhibit nonsense suppression without generation of a stable [PSI+]. Here, we show that in such cells, most of Sup35 represents amyloid polymers, although the remaining Sup35 monomer is sufficient for normal translation termination. The presence of these polymers strictly depends on [PIN+], suggesting that their maintenance relies on efficient generation de novo rather than inheritance. Sup35 polymers contain Rnq1, confirming a hypothesis that Rnq1 polymers seed Sup35 polymerization. About 10% of cells overproducing Sup35 form colonies on medium selective for suppression, which suggests that the proportion of Sup35 monomers to polymers varies between cells of transformants, allowing selection of cells deficient for soluble Sup35. A hybrid Sup35 with the N-terminal domain replaced for 66 glutamine residues also polymerizes and can cause nonsense suppression when overproduced. The described polymers of these proteins differ from the [PSI+] polymers by poor heritability and very high frequency of the de novo appearance, thus being more similar to amyloids than to prions.