We apply the orthonormalization procedure previously introduced by two of us and adopted in connection with coherent states to Gabor frames and other examples. For instance, for Gabor frames we show how to construct g(x) ∈ L2(R) in such a way the functions gn(x) = e 1g(x+an2), n ∈ Z2 and a some positive real number, are mutually orthogonal. We discuss in some details the role of the lattice nat...