Abstract: A noncommutative Jordan Algebra, J, of degree two can be constructed from an anticommutative algebra S that has a symmetric associative bilinear form. If additional conditions are put on the algebra S, information about the derivations and automorphisms of J can be obtained. If S is a n+1 dimensional algebra, and T is a nonsingular linear transformation on S, it is of interest to know what multiplications and what nondegenerate symmetric associative bilinear forms, can be put on S so that T(T(x)T(y))=xy for all x,y,z in S, and T is equal to its adjoint. If T has only one Jordan block the question is answered, in the form of conditions that must be satisfied on the multiplication constants. It is shown such algebras exist for all n and it is shown how to obtain the multiplication tables.