  In this paper we consider Lorentzian surfaces in the 4-dimensional
pseudo-Riemannian sphere $\mathbb S^4_2(1)$ with index 2 of curvature one. We
obtain the complete classification of minimal Lorentzian surfaces $\mathbb
S^4_2(1)$ whose Gaussian and normal curvatures are constants. We conclude that
such surfaces have the Gaussian curvature $1/3$ and the absolute value of
normal curvature $2/3$. We also give some explicit examples.
