Recently, a new and powerful matrix decomposition method has been developed and used in image decomposition for computer vision. The method is recursive, and is based on non-iterative univariate truncations of two variable High Dimensional Model Representation (HDMR). In each step, two vectors in the left and right domains of the target matrix are determined and used in reference vectors of the next step. Each initial reference vector's elements are identical and orthogonality is ensured in the construction. This work brings flexibility to the initialization of the reference vectors and increases the quality of the approximations via decomposition truncation. Certain numerical implementations are also presented for illustration.