We investigate complete minimal hypersurfaces in the
Euclidean space ${R}^{4}$, with Gauss-Kronecker curvature
identically zero. We prove that, if $f:M^{3}\rightarrow
{R}^{4}$ 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.