Cells maintain size homeostasis by coupling growth to division. In budding yeast, newborn cells contain similar amounts of the G1/S inhibitor Whi5, which is diluted as cells grow in G1 to promote cell cycle entry. Similar Whi5 amounts at birth arise from size-independent (sub-scaling) WHI5 mRNA production during S/G2/M and equal partitioning of Whi5 at division. Although chromatin association explains equal partitioning at division, the basis of sub-scaling transcription remained unclear. By systematically mutating the WHI5 promoter, we identify a core region from -126 to -75 bp upstream of the start codon that is responsible for sub-scaling. This sequence contains a repeating array of binding sites for the Fkh1/2 transcription factor. Mutating these sites, deleting FKH1 or FKH2, or disrupting Fkh1/2 dimerization weakens WHI5 sub-scaling. Together with structural predictions and a mathematical model of cooperative Fkh binding, our results suggest that sub-scaling WHI5 transcription is regulated by a Fkh1/2 heteropolymer that binds an array of sites in its core promoter.