  Let $n=2m$, $m$ odd, $e|m$, and $p$ odd prime with $p\equiv1\ \mathrm{mod}\
4$. Let $d=\frac{(p^{m}+1)^{2}}{2(p^{e}+1)}$. In this paper, we study the
cross-correlation between a $p$-ary $m$-sequence $\{s_{t}\}$ of period
$p^{2m}-1$ and its decimation $\{s_{dt}\}$. Our result shows that the
cross-correlation function is six-valued and that it takes the values in
$\{-1,\ \pm p^{m}-1,\ \frac{1\pm p^{\frac{e}{2}}}{2}p^{m}-1,\ \frac{(1-
p^{e})}{2}p^{m}-1\}$. Also, the distribution of the cross-correlation is
completely determined.
