Canonical correlation analysis is an essential technique in many fields such as multivariate statistical analysis and signal processing. In this paper, un-constrained optimization criteria for extracting the actual canonical correlation coordinates are proposed. The resulting gradient dynamical system is thoroughly analyzed in terms of stability and the limiting behavior of the system as t → ∞. One of the main features of this approach is that orthogonal basis for canonical variates which diagonalizes the coherence matrix is automatically obtained. A numerical example is included to demonstrate the performance of the proposed algorithm.