We modify the viscosity to disappear inside the sonic point in the advection-dominated accretion flows (ADAF's) around black holes, and obtain the causally connected, physically self-consistent ADAF-thin disk solutions. Such global solutions differ from previous ones in quantitative details. The results show that the range of variation for the value of the outer boundary R_out is very large, from 30R_g to 10⁶R_g. There is a narrow region for which the rotating motion of the flow is super-Keplerian in each global solution. An example global solution with the causal viscosity is given explicitly, for which R_s = 2.28R_g and j = 1.7564(cR_g).