Navigation is a fundamental cognitive function of virtually all moving animals. Several navigation strategies require an estimate of the current travelling direction that is updated continuously. In the central complex of the insect brain, multimodal cues are fused into a compass-like head direction representation. Based on the proposed connectivity of columnar neurons in the central complex of the desert locust we designed a computational model to examine how these neurons could maintain a stable representation of heading direction and how shifts occur by optic flow signals when the animal turns. Our proposed model architecture shows that the activity of head direction-encoding CL1a neurons remains stable if the activity of a second class of columnar neurons, CL2, is exactly the same. Shifts occur via modulation of the network connectivity. Our model can be used to deduce testable hypotheses where data are lacking, inspiring new avenues of experimental investigations.