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Desert ants (Cataglyphis fortis) navigate by means of path integration, and perform accurately even in undulating terrain. They are able to correctly calculate the ground distance between nest and feeder even if their foraging excursion leads them over corrugated surfaces. To compute the respective ground projection when walking over an inclined surface, ants must measure its slope with sufficient accuracy-but how they do so is still not understood. Using a new behavioural assay that included a negative reinforcement, we investigated how well different slopes are discriminated by the ants. Ants were trained to visit an elevated feeder, via a ramp of fixed inclination (five training inclinations were used: 0A degrees, 15A degrees, 30A degrees, 45A degrees, 60A degrees). The ants discriminated a steeper test slope that differed from the training slope by 12.5A degrees. This discrimination performance was found to be constant for training slopes between 0A degrees and 45A degrees. Ants trained on a 60A degrees slope, however, did not discriminate all steeper slopes, up to a vertical ascent, from the 60A degrees inclination. The consequences of this discrimination accuracy for errors in the path integration process are discussed.