Total Exchange is one of the most important collective communication patterns for scientific applications. In this paper we propose an algorithm called ${\mathcal LG}$ for the total exchange redistribution problem between two clusters. In our approach we perform communications in two different phases, aiming to minimize the number of communication steps through the wide-area network. Therefore, we are able to reduce the number of messages exchanged through the backbone to only 2× max (n 1 ,n 2) against 2×n 1 ×n 2 messages with the traditional strategy (where n 1 and n 2 are the number of nodes of each clusters). Experimental results show that we reach over than 50% of performance improvement comparing to the traditional strategies.