The relative position and orientation parameters between two cameras in a stereo pair are included within the Essential matrix, E. The decomposition of this matrix into a rotation matrix, R, and a skew-symmetric matrix, S, is an efficient tool for retrieving the relative position and orientation of the cameras. In this paper, a new method is proposed to recover these parameters using the singular value decomposition (SVD) of the Essential matrix. First, using the SVD properties, the existing formulas in the decomposition of the Essential matrix into a rotation matrix and a skew-symmetric matrix are directly proved. Then, based on these results, a new method in the decomposition of the Essential matrix using SVD will be presented. The Essential matrix decomposition in this method is accomplished by extracting the base vector of the left null space of the Essential matrix and then followed by SVD decomposition of the skew-symmetric matrix corresponding to this base vector. In this method, the initial mapping of the Essential matrix, recovered from the erroneous coordinates of the corresponding image points in two images, into the space of Essential matrices does not require. The numerical analysis shows that the results of the new presented method are correct and identical with the results of the existing formulas.