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The large number of interconnects in high-speed circuits is a major bottleneck for fast simulation of such circuits. Recently, waveform relaxation methods based on transverse partitioning (WR-TP) were proposed to address this issue. It was shown that the complexity of WR-TP grows only linearly with the number of lines. However, as the coupling between the lines becomes stronger, the WR-TP algorithm either fails to converge or the number of iterations required for convergence increases. In this paper, an overlapping partitioning method for WR-TP is presented, which overcomes the effect of strong coupling between the lines. Numerical examples are presented which demonstrate the accuracy and efficiency of the proposed method for tightly coupled lines.