In [1 ], the orthogonal matrices have been obtained with the aid of Skew-symmetric matrices in E 2 and E3, In addition, an interpretation for these matrices has been given in this paper we tried to give the solution of this problem for En , n > 3. It has been shown in [2 ] that the Lie algebra of the Lie group of orthogonal matrices O(n) consists of the skew symmetric matrices. Here, we explain the orthogonal nxn matrices in terms of the exponential expansion of the bases of skew-symmetric matrices. Consequently we give a factorization of elements of SO(n) in terms of Euler Angles.