  We consider a unit speed timelike curve $\alpha$ in Minkowski 4-space $E_1^4$
and denote the Frenet frame of $\alpha$ by $\{T,N,B_1,B_2\}$. We say that
$\alpha$ is a generalized helix if one of the unit vector fields of the Frenet
frame has constant scalar product with a fixed direction $U$ of $E_1^4$. In
this work we study those helices where the function $<B_2,U>$ is constant and
we give different characterizations of such curves.
