Dyakonov surface waves (DSWs) are electromagnetic surface waves that exist at the interface of two dissimilar materials, with at least one material being anisotropic. Although there are various types of these waves, they all exist in anisotropic materials with positive anisotropy. The requirement for positive anisotropy limits the choice of materials that can support these waves. In this study, we present a type of Dyakonov surface wave that occurs at the interface of negatively anisotropic materials. Specifically, we demonstrate their existence in a system consisting of two negatively anisotropic slabs confined between two perfect electric conductor (PEC) walls. By assuming a small distance between the walls, we derive analytical expressions for the propagation constant, penetration depth, and field distribution of these surface waves. We numerically demonstrate that these surface waves can also exist in structures beyond the approximations used to develop the theoretical framework. The existence of Dyakonov surface waves in negative crystals broadens the range of materials suitable for their practical implementation.