An infinite family of Hadamard matrices with fourth last pivot n/2

We show that the equivalence class of Sylvester Hadamard matrices give an infinite family of Hadamard matrices in which the fourth last pivot is n/2 . Analytical examples of Hadamard matrices of order n having as fourth last pivot n/2 are given for n = 16 and 32. In each case this distinguished case with the fourth pivot n/2 arose in the equivalence class containing the Sylvester Hadamard matrix.