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Besides stability, a high degree of transparency is also an essential requirement in order to enable operators to safely and precisely perform bilateral teleoperation tasks. An existing approach based on the wave transformation technique can make a two-channel teleoperation system insensitive to time delays by making the time-delayed communication channel passive. In this paper, we propose a novel method for incorporating this technique in a four-channel architecture, which is the optimal architecture from a transparency point of view, and derive the corresponding absolute stability condition. It is analytically demonstrated that the proposed teleoperation architecture is capable of providing ideal transparency when transmission delays are present, and criteria for its stable operation are derived. We also show that a three-channel variant of the proposed four-channel control architecture can offer a comparable performance with less implementational complexity. Experimental results in support of the developed theory are provided.