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The lateral force on a rectangular permanent magnet (PM) above a cylindrical high-temperature superconductor (HTS) is numerically calculated during lateral traverses at different cooling heights (CHs). The simulations are based upon the critical state model of Bean. Our simulation results show that the lateral force on the PM is influenced by the initial cooling conditions of the HTS. This conclusion agrees with a previous experimental finding. The calculations show that there is a transition CH. The levitating body is laterally stable when the initial CH is less than the transition CH, whereas, when the initial CH is above the transition CH, the levitating body is possibly laterally unstable. The effects of the dimensions of the system, the physical parameters, and the levitating height during lateral traverses on the transition CH are presented.