Reconfiguration of an interconnection network is fundamental for the provision of a reliable service. Current reconfiguration methods either include deadlock-avoidance mechanisms that impose performance penalties during the reconfiguration, or are tied to the Up*/Down* routing algorithm which achieves relatively low performance. In addition, some of the methods require complex network switches, and some are limited to distributed routing systems. This paper presents a new dynamic reconfiguration method, RecTOR, which ensures deadlock-freedom during the reconfiguration without causing performance degradation such as increased latency or decreased throughput. Moreover, it is based on a simple concept, is easy to implement, is applicable for both source and distributed routing systems, and assumes Transition-Oriented Routing which achieves excellent performance. Our simulation results confirm that RecTOR supports a better network service to the applications than Overlapping Reconfiguration does.