In recent years, routing has been the most focused area in ad hoc networks research. On-demand routing in particular, is widely developed in bandwidth constrained mobile wireless ad hoc networks because of its effectiveness and efficiency. Most proposed on-demand routing protocols however, build and rely on single route for each data session. Whenever there is a link disconnection on the active route, the routing protocol must perform a route recovery process. In QoS routing for wired networks, multiple path routing is popularly used. Multiple routes are however, constructed using link-state or distance vector algorithms which are not well-suited for ad hoc networks. We propose an on-demand routing scheme called Split Multipath Routing (SMR) that establishes and utilizes multiple routes of maximally disjoint paths. Providing multiple routes helps minimizing route recovery process and control message overhead. Our protocol uses a per-packet allocation scheme to distribute data packets into multiple paths of active sessions. This traffic distribution efficiently utilizes available network resources and prevents nodes of the route from being congested in heavily loaded traffic situations. We evaluate the performance of our scheme using extensive simulation.