The author combines known results on functions of conditionally negative type with the definition of a coarse embedding and obtains the following result: A topological group \(G\) with a left \(G\)-invariant metric \(d\) admits a coarse embedding into a Hilbert space \(H\) if and only if there exist a function \(\psi:G\to\mathbb{R}\) conditionally of negative type and non-decreasing functions \(\rho_i:[0,\infty)\to[0,\infty)\), \(i=1,2\), satisfying the conditions (1) \(\rho_1(d(h,g))\leq\psi(g^{-1}h)\leq \rho_2(d(h,g))\) \(\forall g,h\in G\), (2) \(\lim_{t\to\infty}\rho_1(t)=\infty\).