It turns out that one can characterize inner automorphisms without mentioning either conjugation or specific elements. We prove the following Theorem Let G G be a group and let α \alpha be an automorphism of G G . The automorphism α \alpha is an inner automorphism of G G if and only if α \alpha has the property that whenever G G is embedded in a group H H , then α \alpha extends to some automorphism of H H .