A method for monitoring the integrity of an aircraft position computed on board including on-board means for monitoring the aircraft position that are able to detect common-mode failures. Dissimilar computing channels of the aircraft position are utilized, the dissimilar channels being on-board in the aircraft. Each aircraft position primary computing channel is supplemented by a dissimilar computing channel, which allows the coherence of the primary aircraft position, the position computed by the primary computing channels, to be verified. Mechanisms for verifying the reliability of the results from dissimilar computing channels are implemented to limit a loss of performance from the utilization of dissimilar computing channels, which are less performing than primary computing channels.