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In this paper we study an extension of the Bernstein Theorem for minimalspacelike surfaces of the four dimensional Minkowski vector space form and weobtain the class of those surfaces which are also graphics and have non-zeroGauss curvature. That is the class of entire solutions of a system of twoelliptic non-linear equations that is an extension of the equation of minimalgraphic of $\mathbb R^3$. Therefore, we prove that the so-called Bernsteinproperty 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 minimalspacelike surface, and identify the necessary conditions to extend continuouslya local solution of the generalized Cauchy-Riemann equations.

Minimal spacelike surfaces and the graphic equations in R^4_1