Abstract. We present our further observations on the structure of the AES algorithm relating to the cyclic properties of the functions used in this cipher. We note that the maximal period of the linear layer of the AES algorithm is short, as previously observed by S. Murphy and M.J.B. Robshaw. However, we also note that when the non-linear and the linear layer are combined, the maximal period is dramatically increased not to allow algebraic clues for its cryptanalysis. At the end of this paper we describe the impact of our observations on the security of the AES algorithm. We conclude that although the AES algorithm consists of simple functions, this cipher is much more complicated than might have been expected.