In his development of a structure theory for Jordan algebras of characteristic two, E.C. Paige [1] introduces an important class of central simple Jordan algebras S[2n], It is the purpose of this paper to completely determine the automorphism groups of the algebras S[2n]. The automorphisms will be represented as matrices operating on a natural basis for the underlying vector space of the algebra. Using this characterization, generators and relations will be obtained for each of the automorphism groups. In this way, we will produce an infinite family of finite 2-groups.