  Let $d=\frac{(3^{2k}+1)^{2}}{20}$, where $k$ is an odd integer. We show that
the magnitude of the cross-correlation values of a ternary $m$-sequence
$\{s_{t}\}$ of period $3^{4k}-1$ and its decimated sequence $\{s_{dt}\}$ is
upper bounded by $5\sqrt{3^{n}}+1$, where $n=4k$.
