After pointing out the reason why a Finsler space \(F_ n\) has no isometric imbedding into a Riemannian space \(V_ k\), a \(V_{2n}\) is constructed with the aid of \(F_ n\), and a mapping \(\phi\) of the curves \(c_ F\) in \(F_ n\) into the family of curves of \(V_{2n}\) is given. \(\phi\) has certain properties not too far from length preserving. Also a mapping \(\phi\) of Finsler vectors into the vectors of \(V_{2n}\) is given having again properties not too far from preserving parallelity.