  In the paper, the large time behavior of solutions of the Cauchy problem for
the one dimensional fractal Burgers equation $u_t+(-\partial^2_x)^{\alpha/2}
u+uu_x=0$ with $\alpha\in (1,2)$ is studied. It is shown that if the
nondecreasing initial datum approaches the constant states $u_\pm$ ($u_-<u_+$)
as $x\to \pm\infty$, respectively, then the corresponding solution converges
toward the rarefaction wave, {\it i.e.} the unique entropy solution of the
Riemann problem for the nonviscous Burgers equation.
