T. Ikawa obtained the following differential equation
for the circular helix which corresponds the case when the curvature and torsion of space-like curve with a space-like binormal on the Lorentzian manifold are constant [T. Ikawa, Tsukuba J. Math. 9, 353–371 (1985; Zbl 0588.53017)]. In this paper, we define a slant helix with the help of the Bishop frame of the space-like curve with a space-like binormal. Furthermore, we give some necessary and sufficient conditions for the slant helix and T. Ikawa’s result is generalized to the case of the general slant helix.