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Null points are important locations in vector fields, such as a magnetic field. A new technique (a trilinear method for finding null points) is presented for finding null points over a large grid of points, such as those derived from a numerical experiment. The method was designed so that the null points found would agree with any field lines traced using the commonly used trilinear interpolation. It is split into three parts: reduction, analysis, and positioning, which, when combined, provide an efficient means of locating null points to a user-defined subgrid accuracy. We compare the results of the trilinear method with that of a method based on the Poincare index, and discuss the accuracy and limitations of both methods. (C) 2007 American Institute of Physics.