The "Fawkes" procedure is discussed as a method of protection against unauthorized use and recognition of facial images from social networks. As an example, the results of an experiment are given, confirming the fact of a low result of face image recognition within CNN, when the Fawkes procedure is applied with the parameter mode = "high". Based on a comparative analysis with the original images of faces, textural changes and graphical features of the structural destruction of images subjected to the Fawkes procedure are shown. In addition to this analysis, multilevel parametric estimates of these destructions are given and, on their basis, the reason for the impossibility of recognizing images of faces subjected to the Fawkes procedure, as well as their use in deep learning problems, is explained. The structural similarity index (ISSIM) and phase correlation of images are used as quantitative assessment tools. It is also noted that facial images subjected to the Fawkes procedure are well recognized outside of deep learning methods. For this purpose, models of two simple systems for recognizing face images subjected to the Fawkes procedure are proposed, and the results of the experiments performed are presented. It is argued that the use of simple face image recognition systems in a computer complex with CNN will make it possible to train such complexes and destroy the myth about the possibility of protecting face images. In conclusion, the question is posed as to whether it is possible to protect your face from recognition.