Abstract Binary Goppa codes are a large and powerful family of error-correcting codes. But how to find the true minimum distance of binary Goppa codes is not yet solved. This paper will give derivation of a new lower bound for the minimum distance of binary Goppa codes. This new lower bound improves the results obtained by Y. Sugiyama et al. (1976) and Feng Guiliang (1983). The method in this paper can be generalized for other Goppa codes easily.