In a distributed system, one of the most important things is to establish an assignment method for distributing tasks. It is assumed that a dis tributed system does not have a central administrator, all independent processing units in this system want to cooperate for the best results, but they cannot know the conditions of one another. So in order to undertake the tasks in admirable pro portions, they have to adjust their undertaking tasks only by self-learning. In this paper, the performance of this system is analyzed by Markov chains, and a robust method of self-learning for independent processing units in this kind of systems is presented. This method can lead the tasks of the system to be distributed very well among all the independent processing units, and can also be used to solve the general assignment problem. In a distributed system, one of the most important things is to establish an assignment method for distributing tasks. It is assumed that a dis tributed system does not have a central administrator, all independent processing units in this system want to cooperate for the best results. , but they can not know the conditions of one another. So in order to undertake the tasks in admirable pro portions, they have to adjust their undertaking tasks only by self-learning. In this paper, the performance of this system is analyzed by Markov chains , and a robust method of self-learning for independent processing units in this kind of systems is presented. This method can lead the tasks of the system to be distributed very well among all the independent processing units, and can also be used to solve the general assignment problem.