For a spanning tree T of a connected graph ${Gamma}$ and for a labelling ${phi}$: E(T) ${ ightarrow}$ {+,-},${phi}$ is called an alternating sign on a spanning tree T of a graph ${Gamma}$ if for any cotree edge $e{in}E({Gamma})-E(T)$, the unique path in T joining both end vertices of e has alternating signs. In the present article, we prove that any graph has a spanning tree T and an alternating sign on T.