Let \(D\) be a domain in \({\mathbb R}^d\), \(d\geq 3\), and let \(G(x,y)\) be the classical Green function for \(D\). The \(3G\)-inequality states that there is a constant \(C>0\) such that for all \(x,y,z\in D\), \[ {G(x,z)G(z,y)\over G(x,y)}\leq C\left(| x-z| ^{2-d}+| z-y| ^{2-d}\right)\, . \] It is known that the \(3G\)-inequality holds for the uniform domains. In this paper the author shows that the \(3G\)-inequality does not hold for a domain \(D\) containing a spine which is defined by a function \(\phi\) satisfying \(\liminf_{t\to 0}\phi(t)/t=0\).