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Unlike its conventional version, an unconditionally stable alternating-direction-implicit (ADI) finite-difference time-domain (FDTD) method was recently proposed that retains the correct divergence property but with higher computation expenditure. In this letter, a newly formulated divergence-preserved ADI-FDTD method is proposed. It takes about 41.7% less count of floating-point operations than the original divergence-preserved ADI-FDTD method without scarifying accuracy. Detailed analysis and numerical examples are presented to verify the improvement of computational efficiency.