This is a web appendix with supplementary material for the paper “A New Parametrization of Correlation Matrices” by Archakov and Hansen (2020). Here, we present four sets of results: 1) The finite sample properties of γˆ when C has a Toeplitz structure. 2) The finite sample properties of γˆ when C has general (randomly generated) structure. 3) The Jacobian ∂ρ/∂γ for two correlation matrices. One with a Toeplitz structure, and one based on the empirical correlation matrix for returns on 10 industry portfolios. 4) Software implementations of C(γ), that reconstructs C from γ for Julia, Matlab, Ox, Python, and R.