An algorithm is described that can detect and locate some discontinuities and provide information about their size, order and position. However, the success of the algorithm is strongly dependent on the location of the discontinuity with respect to the steps that straddle it. The major advantage of the scheme appears to be that a more reliable error estimate can be used when a discontinuity is present so that codes will be more robust. In some cases significant savings may accrue but it appears that a better restarting procedure than the one used will be necessary to realize most of those benefits.