Conventional TCP fails to achieve optimal TCP performance since it does not handle well the loss of retransmitted segments, generated by the fast retransmit algorithm and the response of partial ACK under fast recovery. This paper introduces an algorithm to recover these lost retransmissions for NewReno TCP and details the steps to implement it. It provides careful retransmission by considering the loss of unacknowledged segments. The algorithm is followed by two options for restoring the congestion control state; both reduce the moderate transmission rate which mitigates network congestion. ns2 simulations show that the algorithm can overcome the loss of retransmitted segments. Moreover, it also suppresses the unnecessary throughput degradation more effectively than is possible with the recovery of lost retransmissions in Reno TCP and equals the performance offered by the SACK-based algorithm. The two options for restoring the congestion control state are also shown to offer adequate performance under retransmitted segment loss.