Bressoud introduced the partition function $B(α_1,\ldots,α_λ;η,k,r;n)$, which counts the number of partitions with certain difference conditions. Bressoud posed a conjecture on the generating function for the partition function $B(α_1,\ldots,α_λ;η,k,r;n)$ in multi-summation form. In this article, we introduce a bijection related to Bressoud's conjecture. As an application, we give a new companion to the Göllnitz-Gordon identities.