This paper is concerned with the asymptotic behavior toward the rarefaction waveuR(x/t) of the solution of the Burgers equation with viscosity. If the initial data are suitably close to constant stateu± atx=±∞, then the solutionu(x, t), roughly speaking, satisfies supR |u −uR| ∼t−1/2 ast → ∞ and, except for the “neighborhoods” of the corners,x=u±t ofuR, sup |u−uR|∼t−1. In the proof the exact forms ofu are available.