We present a method of finding clusters with the property of mutual symmetry of the data pattern structure in parallel coordinates. The description of the method and the implementing algorithm is given. Clear-cut examples of identifying the symmetry of the data structure are considered using the exam-ples of “Balance Scale Data Set”, “Car Data Set”, and “Pollen Data Set” on the one hand, as well as the capabilities and specific aspects of the method for Visual Data Mining purposes on the other hand. The conclusion contains the main results obtained in the course of experimental verification with regard to the properties of the analyzed objects, reflected by the structure of their data.