Fitness landscape rotation has been widely used in the field of dynamic combinatorial optimisation to generate test problems for academic purposes. This method changes the mapping between solutions and objective values, but preserves the structure of the fitness landscape. In this work, the rotation of the landscape in the combinatorial domain is theoretically analysed using concepts of discrete mathematics. Certainly, the preservation of the neighbourhood relationship between the solutions and the alterations of the adaptation of the landscape are studied in detail. Based on the theoretical insights obtained, landscape rotation is used to implement a strategy to escape local optima when local search-based algorithms get stuck. Conducted experiments confirm the efficiency of the landscape rotation applied to local search algorithms for the examination of local optima on the linear ordering problem.