Limited communication range, together with mobility of robots, makes it crucial to design the control plans such that connectivity of a multi-robot network is maintained. Recently, many local and global connectivity maintenance schemes have been proposed to preserve connectivity of a robotic network. The traditional local connectivity maintenance method (LCM) is known to preserve every existing link, even though some of the existing connections might not be necessary for maintaining a path between each pair of robots, which is the aim of global connectivity maintenance (GCM) methods. However, the flexibility of movement provided by the global method costs restriction on speed and bandwidth. In this paper, a modified local connectivity maintenance method is provided to gain more flexibility of movement, while preserving the properties and simplicity of a local method. The proposed method is based on traditional local connectivity maintenance equipped with a basic operation to exchange the neighbors between two adjacent robots. Permutation of robots could be beneficial in many robotic applications such as exchanging the leader role in a V-formed robotic group or providing a path for a robot to reach its desired position while preserving the networks connectivity.