Transformations of real and arbitrary 2 x 2 matrices are employed in parallel algorithms based on Jacobi-like precedures for matrix factorizations like the eigenvalue and the singular value decompositions. Cast in the primitives afforded by the CORDIC algorithms, significant speedup may be achieved in the performance of special-purpose processor array architectures. In this paper, we discuss the use of CORDIC for unitary two-sided 2x 2 matrix transformation. We emphasize integration of evaluation of parameters with application of transformations, using only the primitives afforded by CORDIC. Implementation alternatives are presented in both non-redundant and the redundant and on-line approaches to CORDIC.