The efficiency of stop codons read‐through in yeast is controlled by multiple interactions of genetic and epigenetic factors. In this study, we demonstrate the participation of the Hal3‐Ppz1 protein complex in regulation of read‐through efficiency and manifestation of non‐Mendelian anti‐suppressor determinant [ISP+]. Over‐expression of HAL3 in [ISP+] strain causes nonsense suppression, whereas its inactivation displays as anti‐suppression of sup35 mutation in [isp−] strain. [ISP+] strains carrying hal3Δ deletion cannot be cured from [ISP+] in the presence of GuHCl. Since Hal3p is a negative regulatory subunit of Ppz1 protein phosphatase, consequences of PPZ1 over‐expression and deletion are opposite to those of HAL3. The observed effects are mediated by the catalytic function of Ppz1 and are probably related to the participation of Ppz1 in regulation of eEF1Bα elongation factor activity. Importantly, [ISP+] status of yeast strains is determined by fluctuation in Hal3p level, since [ISP+] strains have less Hal3p than their [isp−] derivatives obtained by GuHCl treatment. A model considering epigenetic (possibly prion) regulation of Hal3p amount as a mechanism underlying [ISP+] status of yeast cell is suggested.