Computer networks generally operate using a single routing protocol. However, there are situations where the routing protocol has to be changed (e.g., because an update of the routing protocol is available, or because an external event has triggered a traffic with different quality of service requirements). In this paper, we show that an uncontrolled change of the routing protocol might yield to transient routing loops (even if the involved routing protocols are loop-free). We show that it is possible to achieve a loop-free change for multiple destinations using a strongly connected component approach producing successive steps, where each step contains nodes that can change the routing protocol in parallel. Our aim is to reduce the number of steps in order to reduce the time required for the network to change from one routing protocol to another. Simulation results show that our strongly connected component approach greatly reduces the number of steps compared to the state of the art, and thus it greatly reduces the time for the change.