The theory of radiation-driven wind including stellar rotation is reexamined. After a suitable change of variables, a new equation for the mass-loss rate is derived analytically. The solution of this equation remains within 1% confidence when compared with numerical solutions. In addition, a nonlinear equation for the position of the critical (singular) point is obtained. This equation shows the existence of an additional critical point besides the standard m-CAK critical point. For a stellar rotation velocity larger than similar to0.7-0.8V(bkup), there exists only one critical point, located away from the star's surface. Numerical solutions crossing through this new critical point are attained. In these cases, the wind has a very low terminal velocity and therefore a higher density. Disk formation in Be stars is discussed in the framework of this new line-driven stellar wind solution.