This paper presents a new mirroring-and-registration method for the automatic symmetry plane detection of 3D asymmetrically scanned human faces. Once the mirroring of the original data is carried out with respect to the first-attempt symmetry plane, which is estimated by the PCA method, the source point cloud and the mirrored data are registered by the ICP algorithm that minimises a new weighted function. The final symmetry plane obtained approximates in the least-squares sense the midpoints of the lines connecting homologous points randomly chosen. This method is validated by analysing some specifically-designed test cases. The obtained results show that the method is quite insensitive to asymmetries of data resulting from the acquisition process.