  In this paper, we obtain some properties of biconservative Lorentz
hypersurface $M_{1}^{n}$ in $E_{1}^{n+1}$ having shape operator with complex
eigen values. We prove that every biconservative Lorentz hypersurface
$M_{1}^{n}$ in $E_{1}^{n+1}$ whose shape operator has complex eigen values with
at most five distinct principal curvatures has constant mean curvature. Also,
we investigate such type of hypersurface with constant length of second
fundamental form having six distinct principal curvatures.
