  We investigate complete minimal hypersurfaces in the Euclidean space $% \
{R}^{4}$, with Gauss-Kronecker curvature identically zero. We prove that, if
$f:M^{3}\to {R}^{4}$ is a complete minimal hypersurface with Gauss-Kronecker
curvature identically zero, nowhere vanishing second fundamental form and
scalar curvature bounded from below, then $f(M^{3})$ splits as a Euclidean
product $L^{2}\times {R}$, where $L^{2}$ is a complete minimal surface in $
{R}^{3}$ with Gaussian curvature bounded from below.
