A substitution for the aperiodic hat monotile found in 2022 and published in SMCG2023, see also BGS2023. The “metatiles” in the first paper have some free parameter. Most of these parameters yield a substitution that is not selfsimilar. Here we show the selfsimilar version of the substitution rule. This tiling was used to derive the cut-and-project description of the hat tiling in BGS2023.