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 $\mathbb{ E}_2^4$.
Categories: math.DG