We present a new least squares technique for the determination of axis orientation, motion, and intrinsic axial electric field for two-dimensional coherent structures in a space plasma. This single-spacecraft method is based on Faraday's law, which, under the model assumptions, requires the intrinsic axial electric field to be constant in space and time. The technique is applied to two flux transfer events seen by the four Cluster spacecraft, although data from only one of them (Cluster 1) is used in the analysis. For these events, excellent agreement is found with the orientations obtained from optimal Grad-Shafranov reconstruction (Hasegawa et al., 2005), a method that uses data from all four Cluster spacecraft. However, the new method can also fail to produce such agreement. It must therefore be used with caution.