  In this paper, it is proved that, no special timelike Frenet curve is a
Bertrand curve in $\mathbb{E}_2^4$ and also, in $\mathbb{E}_\nu^{n+1}$ $ ({n
\ge 3})$, such that the notion of Bertrand curve is definite only in
$\mathbb{E}_1^2$ and $\mathbb{E}_1^3$. Therefore, a generalization of timelike
Bertrand curve is defined and called as timelike (1,3)-Bertrand curve in
$\mathbb{E}_2^4$. Moreover, the characterization of timelike (1,3)-Bertrand
curve is given in $\mathbb{E}_2^4$.
