Given recent events, training during quarantine can only take place remotely. To ensure quality training, communication must be seamless. To do this, the network must function smoothly. The solution to this problem is functionally stable networks that allow uninterrupted transmission of information due to redundancy. An important issue is the definition of redundancy. To solve this problem, the article considers the method of synthesis of the structure of the distance learning system. The method of synthesis of network structure used for providing distance learning by the criterion of maximum functional stability on the basis of the introduction of correcting communication lines is offered. With this method, you can develop tools for self-recovery of distributed software, taking into account the characteristics of disparate computer resources through the use of redundancy. This will allow you to develop functionally stable software systems, significantly reduce the recovery time of such systems after or in the event of possible failures. To increase the efficiency of the developed method, the mathematical model of the hyper network based on two hypergraphs was improved, which allows taking into account different requirements for the quality of the network.