Abstract: In independent component analysis (ICA) problems, it is the key to find an orthogonal matrix to throw away high-order redundancy between components. Orthogonal matrixes have special structures in which row vectors of them can be seen as vectors perpendicular to each other on N-sphere. A parametrization method of all the matrices of any dimensions is proposed and the completeness of the parametric presentation is proven. Further, a theoretical analysis is made for randomicity. We use genetic algorithm (GA) in searching of the optimized separating matrix. Finally, some numerical simulation results are given.