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Blind source separation (BSS) is the problem of reconstructing unobserved, statistically independent source signals from observed linear combinations thereof. An emerging tool for BSS is the second generalized characteristic function (SGCF), as demonstrated, e.g., by the characteristic-function enabled source separation (CHESS) algorithm (Yeredor (2000)). CHESS achieves separation by applying approximate joint diagonalization to a set of estimated second derivative matrices (Hessians) of the SGCF at pre-selected "processing points". An optimization scheme for the CHESS algorithm, based on solving an optimally weighted least-squares (LS) problem, is proposed in this paper. First, it is shown that the approximate joint diagonalization of the Hessians can be formulated as a nonlinear least-squares model. Then, a scheme for a consistent estimator of the optimal weight matrix is proposed. Next, an iterative algorithm for solving the WLS scheme is presented and demonstrated in simulation.