Abstract: For the nonlinear schrodinger equation iu_t+u_xx+2|u|²u=0, the writer once obtained a new periodic solution q(x, t). In this paper, we will discuss some properties of q(x, t), get all the main spectrum and the auxiliary spectrum of q(x, t), and analyse motion forms of the spectra. We will also prove that q(x, t) is an one-band potential.