We introduce a theoretical algorithm and its practical version to perform decentralized detection of the global convergence of parallel asynchronous iterative algorithms. We prove that even if the algorithm is completely decentralized, the detection of global convergence is achieved on one processor under the classical conditions. The proposed algorithm is very useful in the context of grid computing in which the processors are distributed and in which detecting the convergence on a master processor may be penalizing or even impossible as in Peer to Peer computations framework. Finally, the efficiency of the practical algorithm is illustrated in a typical experiment.