A surgical staple insertion system for compressing bone fragments includes a staple and an insertion tool. The staple has first and second legs and an elastically deformable bridge monolithically formed with the first and second legs. In a relaxed configuration, the free ends of the first and second legs are positioned closer to one another than are portions of the first and second legs connected to the bridge. The insertion tool retains the bridge in an elastically deformed configuration with the legs positioned relatively farther apart from one another during at least portion of the step of implantation of the staple. Then, the insertion tool is released from the staple so that the bone fragments between the legs are subject to compression.