A new type of CNN associative memory called the Autonomous ratio-memory Cellular Nonlinear Network (ARM-CNN) is proposed and analyzed. In the proposed ARMCNN, the input noisy patterns are sent into the cells as the initial cell state voltages. The proposed ARMCNN has the advantages of higher recognition rate (RR), higher number of learned and recognized patterns, and smaller signal ranges of cell state voltages. The RR of the ARMCNN is also modeled as the integration of the probability functions in the convergent regions of the phase plane plot of cell state voltages. Theoretical calculation results are consistent with simulation results.