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In applying the Markov approach to evaluating the mean life of repairable systems, the matrix of state equations is often badly conditioned for inversion. This is especially true for systems with 2-state weather models and/or a broad range of failure and repair rates. If the matrix is inverted by pivoting, accuracy is lost through subtractive cancellation. The paper describes a simple modification to the Gauss-Jordan method which avoids this accuracy loss. On test, this modified method has given fully accurate solutions, where other techniques have given very poor accuracy.