A circulant graph with n nodes and jumps j1, j2, ..., jm is a graph in which each node i, 0 i n - 1, is adjacent to all the vertices i ? jk mod n, where 1 k m. A binomial graph network (BMG) is a cir- culant graph where jk is the power of 2 that is less than or equal to n. This paper presents an optimal (short- est path) two-terminal routing algorithm for BMG net- works. This algorithm uses only the destination address to determine the next hop in order to stay on the short- est path. Unlike the original algorithms, it does not require extra space for routing tables or additional in- formation in the packet. The experimental results show that the new optimal algorithm is significantly faster than the original optimal algorithm.