The heat treatment techniques are significant methods for improving metals and alloys. Particularly, it is important to control transformation temperature and improve mechanical and physical properties of materials. There are two important parameters that can be controlled, which are temperature and time of aging. In this study, a quaternary Cu-79-Al-12-Ni-4-Nb-5 (wt%) alloy was produced using arc melting under an atmosphere control. The alloy was aged isothermally at 1073 K for 1, 2, 3, 6, 12, and 24 h. The map of constituents showed that neither Cu contributed in Nb-rich phases nor Nb dissolved in the matrix. The martensitic phase transformation for as-casted and aged specimens was carried out using a DSC device. The phase transformation was generally shifted to the higher temperature by increasing the time of aging, but the alloy lost its shape memory feature when it was aged for 24 h. XRD and optical microscopy were utilized to investigate characterizations of the alloy. Additionally, the aging introduced multiphases in the alloys and the intensity of XRD peaks was increased by increasing the time of aging up to 3 h.