This paper describes a new mathematical model that is based on centred loops to reconstruct the "Systematic Search" behaviour of Cataglyphis desert ants. The notable advantage of this model is the combination of simplicity, efficiency and performance. All model input is kept to a minimum, using only parameters that previous research has shown to be available to the animals at all times: distance from the origin, direction of the last step and home vector. Outbound and inbound search paths are being combined into loops that return to the origin, sampling this area more intensely. A stochastic element is added by random perturbations during the next step, mimicking unsystematic errors during the process of path integration and yielding the typical search patterns observed in Cataglyphis desert ants. The model output is compared to runs observed in the field.