We propose a practical formulation of the overlap Dirac operator in lattice QCD that employs the diagonal Kenney-Laub rational iterates - expressed via their partial fraction decomposition - to approximate the matrix sign function. We investigate this approximation using the Brillouin operator as kernel, in addition to the standard Wilson Dirac operator. Numerical results show improved chiral symmetry preservation and computational efficiency compared to the Chebyshev polynomial approach.