In this paper the algorithm to search a minimum set of tearing variables in a directed graph has been improved and generalized in such a way as to produce the totality of covering sets. The presented algorithm, which is based on the relation existing between the graph on study and a system of formal equation, has been properly divided into several operating parts to find out in the earliest phases and with short computation times, a large number of minimum covering sets. A number of examples are added, one of them dealing with an industrial chemical plant, in order to have a concrete insight of the adopted algorithm and operating procedure.