  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 $g(x)\in
L^2(\Bbb{R})$ in such a way the functions $g_{\underline
n}(x)=e^{ian_1x}g(x+an_2)$, $\underline n\in\Bbb{Z}^2$ and $a$ some positive
real number, are mutually orthogonal. We discuss in some details the role of
the lattice naturally associated to the procedure in this analysis.
