Exploration of space plays an important role in many animals, in particular for social insects who have to feed and protect a whole colony. In a laboratory study, Khuong et al (2013) studied how the workers of the black garden ant Lasius niger move around in an unknown environment. They assumed that, in a homogeneous arena with no visual cues, ants had no information about their position in space. Based on this hypothesis, they modelled their ants in a Boltzmann Walker framework which describes an ant\'s random walk as a series of straight segments separated by reorientation events. They assumed that on plain horizontal surfaces the ant\'s direction of movement would not influence their average speed, segment lengths and reorientation decisions, thus leading to diffusive trajectories. However, published experiments indicate that L. niger ants are not completely devoid of directional information even in standard laboratory setups with no obvious landmarks. Moreover, many ant species are known to develop specific search strategies when they want to find a particular place in space, a situation that may apply to the analysed data. We re-analyze Khuong et als data on non-inclined surfaces, this time taking into account the ant\'s orientation in relation to its starting point in the arena. We discovered that, with this information taken into account, the ant\'s trajectory is biased towards its starting point (biased random walk), revealing an advecto-diffusive process. In fact, the distributions of segment lengths and reorientation angles turned out to be modulated by the ant\'s orientation in relation to its starting point. By simulating these biased trajectories, we show that this modulation halves the time it takes for an ant to come back towards its starting point. We conclude that not taking into account the animal\'s cognitive abilities in data analysis may lead to incomplete or biased conclusions. The discovered search behaviour in L. niger can play a significant role in the colony\'s exploration and foraging ecology.