  In this paper we study an extension of the Bernstein Theorem for minimal
spacelike surfaces of the four dimensional Minkowski vector space form and we
obtain the class of those surfaces which are also graphics and have non-zero
Gauss curvature. That is the class of entire solutions of a system of two
elliptic non-linear equations that is an extension of the equation of minimal
graphic of $\mathbb R^3$. Therefore, we prove that the so-called Bernstein
property does not hold in general for the case of graphic spacelike surfaces in
$\mathbb R^4_1$. In addition, we also obtain explicitly the conjugated minimal
spacelike surface, and identify the necessary conditions to extend continuously
a local solution of the generalized Cauchy-Riemann equations.
