In this paper, orthonormal eigenvectors of high order power of photon annihila.tion operator are constructed with N basic vectors of coherent states |aei(2π)/N n〉(n = 0,1,2, …,N-1), and squeezing and antibunching in these states are studied. The results show that squeezing appears only when N = 2 and 4 but antibunching exists for every N.