Imbedding of pseudo-Riemannian manifolds in a pseudo-euclidean space

It is proved that every pseudo-Riemannian manifold $M^n_{(p,q)}$ with the $C^k$ metric ($3\leqslant k\leqslant\infty$) has an isometric $C^k$ imbedding in the large in $E_{(p',q')}^{n(n+1)(3n+11)/2}$, $p'\geqslant(n+1)^2$, $q'\geqslant(n+1)^2$.