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A new high-order conformal FDTD(2,4) scheme is proposed to solve the electromagnetic scattering from 3-D curved perfectly conducting objects. For electric field components, the update equations do not need to be modified. For magnetic field components, the inner loop is treated with the locally conformal technique, and the outer loop is unmodified. Numerical results demonstrate that the high-order conformal scheme can obtain better numerical precision under coarse grid condition compared with the low-order conformal method and the high-order staircasing approach, which in turn saves CPU time and memory.