  In this paper, we study Lorentzian hypersurfaces in Minkowski 5-space with
non-diagonalizable shape operator whose characteristic polinomial is
$(t-k_1)^2(t-k_3)(t-k_4)$ or $(t-k_1)^3(t-k_4)$. We proved that in these cases,
a hypersurface is biharmonic if and only if it is minimal.
