Ridesharing is a mobility concept in which a trip is shared by a vehicle’s driver and one or more passengers called riders. Ridesharing is considered as a more environmentally friendly alternative to single driver commutes in pollution-creating vehicles on overcrowded streets. In this paper, we present the core of a new strategy of the ridesharing system, making it more flexible and competitive than the recurring system. More precisely, we allow the driver and the rider to meet each other at an intermediate starting location and to separate at another intermediate ending location not necessarily their origins and destinations, respectively. This allows to reduce both the driver’s detour and the total travel cost. The term “