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The chief shortcoming of the conformal finite-difference time-domain (CFDTD) method is the global time-step reduction in order to avoid instability arising from small irregular cells. In this letter, we introduce a new conformal scheme to overcome this problem for the CFDTD method. The time-step reduction is applied only locally to the small irregular cells, which is only 1/3 of that in the regular cells. In order to update the electric field at the interface between the small irregular cell and its adjacent cells, extra magnetic fields next to the small irregular cell are introduced. Through this scheme, the time-step reduction is limited to a few small cells, and the numerical simulation can be the most efficiently implemented in the FDTD framework. Numerical accuracy is verified by comparison with the conventional CFDTD method for the radar cross section (RCS) of perfect conducting curved objects.