This paper concerns the problem of self-diagnosis of fault-tolerant multiprocessor systems, namely, the determining of processor states after performing all specified mutual checks of processors. The problem is of particular importance for systems with irregular connections. In practice, the regularity of connections is disrupted when developers incorporate new processors into the system along with their associated connections. The formal method of determining states of processors of a \(M\) -diagnosable system with arbitrary diagnostic connections during its testing has been considered. The method essentially comes down to generating a Boolean expression, the complexity of which depends on the number of diagnostic tests performed and their results. An improvement to the method that reduces the complexity of obtaining the Boolean expression in the canonical disjunctive normal form has been proposed. This allows to simplify analyzis of test results and reduce the time for its execution, consequently diminishing overall testing duration and enhancing the capacity of the system to execute primary tasks. The latter is of paramount importance, as testing is a continuous process throughout system operation.