  In this article, we have derived the following Leray-Trudinger type
inequality on a bounded domain $\Omega$ in $\mathbb{R}^n $ containing the
origin. \begin{align*} \displaystyle{\sup_{u\in W^{1,n}_{0}(\Omega),
I_{n}[u,\Omega,R]\leq 1}}\int_{\Omega}
e^{c_n\left(\frac{|u(x)|}{E_{2}^{\beta}(\frac{|x|}{R})}\right)^{\frac{n}{n-1}}}
dx < +\infty \ \text{, for some } c_n>0 \ \text{depending only on } n.
\end{align*} Here $\beta = \frac{2}{n}$, $I_n[u,\Omega,R] :=
\int_{\Omega}|\nabla u |^{n}dx-
\left(\frac{n-1}{n}\right)^{n}\int_{\Omega}\frac{|u|^{n}}{|x|^{n}E_{1}^n(\frac{|x|}{R})}dx
$, $R \geq \displaystyle{\sup_{x\in \Omega}}|x|$ and $E_{1}(t) :=
\log(\frac{e}{t})$, $E_{2}(t) := \log(eE_1(t))$ for $t\in (0,1].$ This improves
an earlier result by Psaradakis and Spector. Also we have proved that, for any
$c>0$ the above inequality is false, if we take $\beta < \frac{1}{n}.$
