The matrix (formula presented), has gained importance lately due to its role in powers preserving total nonnegativity. We give an explicit decomposition of S in terms of elementary bidiagonal matrices, which is analogous to the Neville decomposition. We give a bidiagonal decomposition of (formula presented) for positive integers (formula presented). We also explore the total positivity of Hadamard powers of another important class of matrices called mean matrices. © 2022, Element D.O.O.. All rights reserved.