Let \({\mathcal K}^ n\) be the family of all convex bodies in \(R^ n\) (endowed with the Hausdorff distance \(\rho)\). For \(K\in {\mathcal K}^ n\), let w(K) be the intrinsic width and s(K) the Steiner point of K. Set \({\mathcal K}^ n_*=\{K\in {\mathcal K}^ n: w(K)=2,\quad s(K)=0\}.\) Then \(K\subset B\) for each K in \({\mathcal K}^ n_*\) (B is the unit ball in \(R^ n)\) and \(diam {\mathcal K}^ n_*=1.\) Hence, for \(K_ 0\), \(K_ 1\) in \({\mathcal K}^ n\), we have \(\rho (K_ 0,K_ 1)\leq \max \{w(K_ 0),w(K_ 1)\}+\| s(K_ 0)-s(K_ 1)\|.\)