One key aspect of epigenetic inheritance is that chromatin structures can be stably inherited through generations after the removal of the signals that establish such structures. In fission yeast, the RNA interference (RNAi) pathway is critical for the targeting of histone methyltransferase Clr4 to pericentric repeats to establish heterochromatin. However, pericentric heterochromatin cannot be properly inherited in the absence of RNAi, suggesting the existence of mechanisms that counteract chromatin structure inheritance. Here, we show that mutations of components of the INO80 chromatin-remodeling complex allow pericentric heterochromatin inheritance in RNAi mutants. The ability of INO80 to counter heterochromatin inheritance is attributed to one subunit, Iec5, which promotes histone turnover at heterochromatin but has little effects on nucleosome positioning at heterochromatin, gene expression, or the DNA damage response. These analyses demonstrate the importance of the INO80 chromatin-remodeling complex in controlling heterochromatin inheritance and maintaining the proper heterochromatin landscape of the genome.