  We consider Riemann's Xi function $\xi(s)$ which is evaluated at $s =
\frac{1}{2} + \sigma + i \omega$, given by $\xi(\frac{1}{2} + \sigma + i
\omega)= E_{p\omega}(\omega)$, where $\sigma, \omega$ are real and compute its
inverse Fourier transform given by $E_p(t)$. We study the properties of
$E_p(t)$ and a promising new method is presented which could be used to show
that the Fourier Transform of $E_p(t)$ given by $E_{p\omega}(\omega) =
\xi(\frac{1}{2} + \sigma + i \omega)$ does not have zeros for finite and real
$\omega$ when $0 < |\sigma| < \frac{1}{2}$, corresponding to the critical strip
excluding the critical line.
