  We show that $(g_2,a,b)$ is a Gabor frame when $a>0, b>0, ab<1$ and
$g_2(t)=({1/2}\pi \gamma)^{{1/2}} (\cosh \pi \gamma t)^{-1}$ is a hyperbolic
secant with scaling parameter $\gamma >0$. This is accomplished by expressing
the Zak transform of $g_2$ in terms of the Zak transform of the Gaussian
$g_1(t)=(2\gamma)^{{1/4}} \exp (-\pi \gamma t^2)$, together with an appropriate
use of the Ron-Shen criterion for being a Gabor frame. As a side result it
follows that the windows, generating tight Gabor frames, that are canonically
associated to $g_2$ and $g_1$ are the same at critical density $a=b=1$. Also,
we display the ``singular'' dual function corresponding to the hyperbolic
secant at critical density.
