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PEC or material discontinuity is a challenge to any higher-order FDTD algorithm. In this paper, we develop a new FDTD algorithm relating to the integration loop. This new algorithm has a lower phase error compared to the S24 (second-order-in-time and fourth-order-in-space) method and avoids the crossing of any PEC barrier by using alternative integration path. A cavity resonator is simulated as an illustration of effectiveness of the algorithm and numerical results are compared to those obtained by Yee's method.