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