In this paper we apply angle recoding to the CORDIC-based processing elements in a scalable architecture for complex matrix inversion. We extend the processing elements from the scalable real matrix inversion architecture to the complex domain and obtain the novel scalable complex matrix inversion architecture, which can significantly reduce computational complexity. We rearrange the CORDIC elements to make one half of the processing elements simple and compact. For the other half of the processing elements, the efficient use of angler recoding reduces the number of microrotation steps of the CORDIC elements to 3/4. Consequently, only 3 CORDIC elements are required for the processing elements with full utilization.