A new method for designing stellarators with variable-thickness perpendicular permanent magnets has been developed, based on a two-step magnet design strategy that we previously proposed for designing stellarators with standardized magnet blocks. Our design strategy uses a 'local compensation' method to obtain an initial magnet design and a 'global fine-tuning' method to further optimize the initial design. The new method is compared to the previously proposed Fourier decomposition method, and the results indicate that this new method can yield a similar magnet design for an Nfp = 2 quasi-axisymmetric stellarator at a lower computational cost. High accuracy is achieved, as demonstrated by a normal magnetic field square on the plasma surface of , a maximum residual of for a ∼1 T total field, and a flux-surface-averaged residual Bn of relative to the total field. Furthermore, the new method can automatically yield a magnet design with large areas of continuous vacancies for ports and plasma access, which is more flexible than the Fourier decomposition method. These results indicate that the new method is robust and effective when used to design stellarators with variable-thickness perpendicular permanent magnets, and, most importantly, that the two-step magnet design strategy has great potential to develop permanent magnet design methods suitable for various magnet layouts.