Shape memory alloys (SMAs) represent an exceptional class of smart materials as they are able to recover their shape after mechanical deformation, making them suitable for use in actuators, sensors and smart devices. These unique properties are due to the thermoelastic martensitic transformation that can occur during both thermal and mechanical deformation. Cu-based SMAs, especially those incorporating Al and Ag, are attracting much attention due to their facile production and cost-effectiveness. Among them, Cu-Al-Ag SMAs stand out due to their notably high temperature range for martensitic transformation. In this study, a Cu-based SMA with a new ternary composition of Cu-10Al-7Ag wt.% was prepared by arc melting and the samples cut from this casting alloy were quenched in water. Subsequently, the phase composition and the development of the microstructure were investigated. In addition, the morphology of the martensite was studied using advanced techniques such as electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). The analyzes confirmed the presence of martensitic structures in both samples; mainly 18R (β1′) martensite was present but a small volume fraction of (γ1′) martensite also was noticed in the as-quenched sample. The observation of fine, twinned martensite plates in the SMA alloy with symmetrically occurring basal plane traces between the twin variants underlines the inherent correlation between microstructural symmetry and the properties of the material and provides valuable insights into its behavior. The hardness of the quenched sample was found to be lower than the as-cast counterpart, which can be linked to the solutioning of Ag particles during the heat treatment.