This technical communique represents a generalization of the convergence analysis for the consensus algorithm proposed in Priolo et al. (2014). Although the consensus was reached for any strongly connected weighted digraphs (SCWD), the convergence analysis provided in Priolo et al. (2014) was only valid for diagonalizable matrices encoding a SCWD. The result we present here generalizes the previous one to all possible matrices encoding a SCWD that can be used in the algorithm. (C) 2015 Elsevier Ltd. All rights reserved.