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The use of the minimum singular value (MSV) of the load flow Jacobian has been proposed as a security index for monitoring how close the operating condition of a power system is to a voltage instability. However, direct computation of singular value decomposition (SVD) is a very time consuming task. P.A. Lof et al. (see IEEE Trans. on Power Systems, vol.7, no.1, p.54-64, 1992) report on an elegant and an efficient algorithm for the computation of the MSV of the load flow Jacobian matrix (LFJM). This algorithm greatly reduces the time required for the computation of the MSV. In this letter, a new starting condition that reduces the computation time for the iterative process described by Lof et al. is proposed.