A number of position-based routing protocols have been proposed for mobile ad-hoc networks (MANETs) based on a virtual two-dimensional grid partitioning of the geographical region of the MANET. Each node is assumed to know its own location in the grid based on GPS positioning. A node can also find out the location of other nodes using location services. Selected gateway nodes handle routing. Only the gateway node in a cell contributes to routing packets through that cell. This paper shows how to construct cell-disjoint paths in such a two-dimensional grid. These paths can be used for routing in parallel multiple data packets from a source node to a destination node. They provide alternative routes in cases of routing failures and allow fast transfer of large amounts of data by simultaneous transmission over disjoint paths. Performance characteristics of the constructed paths are derived showing their attractiveness for improving the reliability and speed of communication in MANETs.