On the basis of Ritter real morphological associative memory (RMAM), complex lattices and complex rings are defined respectively through introducing two ordinal relationships between complex numbers, consequently the same recall rules are obtained as RMAM in complex domain and construct a class of complex MAM (CMAM), called extended RMAM. The CMAM can directly process complex signals such as FFT-ed complex data. In this paper, the convergence of the proposed model is proved, its error-correction capability and storage capacity are analyzed,and at the same time the corresponding theorems and properties similar to the RMAM are obtained.Further the difference between the CMAM andother neural networks such as Hopfield network is stressed.The carried-out computer simulations show its feasibility.