The paper presents task decomposition and allocation method for multi-robot systems for area coverage tasks. The method is based on the notion of responsibility area which is the part of the environment that is considered to be atomic task which is allocated to a single robot. The responsibility areas are defined based on the equality of the needed amount of work for their processing. The amount of work is calculated based on the particular area and obstacles in it. The task allocation is done in the way that the most suitable responsibility areas are sequentially added to each robot. The main criterion for the task allocation is the distance from the responsibility area to the particular robot. Still the indexing mechanism is introduced to make the robots to process the environment region by region without leaving unprocessed responsibility areas. The method is implemented and tested in the multi-robot system for vacuum cleaning of large areas that cannot be cleaned by a single vacuum cleaning robot.