Dual-pole Line Start Synchronous Motors (LSSMs) can potentially replace induction motors in two-speed applications such as desert coolers. This article presents a new design of the dual-pole (4/8p) synchronous motor based on the modified structure of the interior Permanent Magnets (PMs). In this design, rather than using a series magnetic structure, a series-parallel structure is proposed. This reduces the equivalent air gap and utilizes the PMs in the rotor core more effectively, since the 8-pole PMs are not located along the flux path of the 4-pole PMs. In addition, the proposed design strengthens the 4-pole reluctance nature of the motor, which further improves the motor's high-speed performance. Overall, the motor exhibits a better transient and steady state performance in both operating speeds with respect to the reference design. For further verification, the Finite Element Analysis (FEA) simulation results are validated by experimental measurements.