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In this paper we prove a new capacity upper bound for a class of relay channels known as Relay-With-Delay channels. The proposed bound is general and holds for any arbitrary amount of delay. We have shown that the previously introduced bounds can be considered as special cases of our proposed upper bound. The new introduced bound is, in some cases, tighter than the previously established bounds. It is also notable that the proposed bound coincides with the previously known capacity of Â¿Relay-With-DelayÂ¿ channels.