New techniques of capturing shape geometry for the purpose of studying asymmetry in biological objects bring the need to develop new methods of analyzing such data. In this paper we propose a method of mesh asymmetry analysis and decomposition intended for use in geometric morphometry. In geometric morphometry the individual bilateral asymmetry is captured by aligning a specimen with its mirror image and analyzing the difference. This involves the construction of a dense correspondence mapping between the meshes. We tested our algorithm on real data consisting of a sample of 102 human faces as well as on artificially altered meshes to successfully prove its validity. The resulting algorithm is an important methodological improvement which has a potential to be widely used in a wide variety of morphological studies.