The structures and magnetic properties of Fe78Si9B13 amorphous ribbons were detected after annealing at different temperatures. Compared with the clusters in the FeB amorphous alloy, the second shell of BB coordination is replaced by SiB coordination in the clusters of the Fe78Si9B13 amorphous alloy. The interaction between Fe and B atoms is strengthened at a higher annealing temperature. Based on the Gaussian decomposition toward the splitting second peaks in g(r) curves, the shared connection modes of the clusters have been obtained. The main connection modes between the clusters of all the samples are the three-atom-shared connection and the one-atom-shared connection. With the increasing annealing temperature, the three-atom-shared connection is enhanced, and the one-atom-shared connections are weakened. Combined with the results of the magnetic hysteresis curves, it is found that the enhancement of the three-atom-shared connection is responsible for the increase of the saturation magnetization.