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This paper presents a method for cooperation in the construction of Voronoi diagrams which is suitable for use in dangerous tasks performed by a team of robots. The algorithm has been implemented on a network of eight workstations using the MPI library. Two implementation approaches have been used. In the first one, no communication among the robots is required but some degree of redundancy in the work performed by the robots may result. In the second approach, a more cooperative scheme is adopted and, as a consequence, communication among the robots increases but the work performed by each one is reduced. In both approaches, the calculation time decreases almost linearly when adding robots to the team. Nevertheless, the second approach, more cooperative, has consistently produced better results. With the achieved speed-up, it is possible to use this algorithm in applications where the obstacle configuration within the robot team working area changes with time.