  In this paper we give Weierstrass-type representation formulas for the null
curves and for the minimal Lorentz surfaces in the Minkowski 3-space $\mathbb
R^3_1$ using real-valued functions. Applying the Weierstrass-type
representations for the null curves, we find a correspondence between the null
curves in $\mathbb R^4_2$ and the pairs of null curves in $\mathbb R^3_1$.
Based on this correspondence, we obtain a relation between the minimal Lorentz
surfaces in $\mathbb R^4_2$ and the pairs of minimal Lorentz surfaces in
$\mathbb R^3_1$.
