This paper employs the add-and-subtract technique of the auxiliary receiver approach to establish a new upper bound for the distributed hypothesis testing problem. This new bound has fewer assumptions than the upper bound proposed by Rahman and Wagner, is at least as tight as the bound by Rahman and Wagner, and can outperform it in certain Gaussian settings. Conceptually speaking, unlike Rahman and Wagner, who view their additional receiver as side information, we view it as an auxiliary receiver and use a different manipulation for single-letterization.