Аннотация: The article discusses the issues related to the modified transformations of Jordan-Gauss when they are used in solving linear equation systems and solving the problems of linear programming by the simplex method. It is proposed to use as a transformation the application of modified transformations of Jordan-Gauss twice and to call such a transformation a double step of modified transformations of Jordan-Gauss. For the double step of the modified Jordan-Gauss transformations, the conditions under which it can be used are formulated, as well as its features and capabilities.