We consider the classical two machine flow shop scheduling problem, with total tardiness criterion. This problem is strongly NP-hard and literature contains already some lower bounds and dominance conditions. The more recent lower bound of the literature is due to Pan Chen and Chao (COR 2002) and is an improvement of the lower bound proposed by Pan and Fan (IJSE, 1997), Kim (COR 1993) and Sen Dileepan and Gupta (COR 1989). We propose here a new lower bound. Computational experiments show that this bound allows to obtain better results, both in terms of generated nodes and computation time.