Nowadays, Peer-to-Peer (P2P) networks play an essential role in large scale live video transmission. Though many algorithms have been proposed to deal with packet loss in P2P networks, there is still a lack of mechanisms dealing with the delay and loss constraints of live video streaming. In this paper, we propose a new loss recovery mechanism allowing the quality optimization of live video transmitted on P2P networks. Its principal feature consists in request retransmission of lost packets from a peer different of the original packet sender. This mechanism increases the probability of choosing the best available peer to make the retransmission and hence, improves the received video quality before its display time. We show by simulations that the proposed solution is efficient in comparison with the current retransmission mechanisms. This solution is independent from the sender peer selection used algorithm.