We show that , unlike the results presented previously in the literature , the transition from an outer Shakura-Sunyaev disk ( SSD ) to an advection-dominated accretion flow ( ADAF ) is possible for large values of the viscosity parameter \alpha > 0.5 . The transition is triggered by thermal instability of a radiation-pressure-supported SSD . The transition radius is close to the central black hole . We confirm our qualitative prediction by actually constructing global bimodal SSD-ADAF solutions .