Radially linked star-block-linear polystyrenes, star-shaped polymers with star-shaped branching at the ends of each arm, were synthesized by the convergent living anionic polymerization method. These novel structurally modified polymers were synthesized by sequential addition of a specific coupling agent, 4-(chlorodimethylsilyl)styrene (CDMSS), styrene, and CDMSS again to a solution of living polystyrene. Through a convergent process, the addition of the coupling agent to the living polystyrene solution resulted in star-shaped polymers with a hyperbranched core containing a single living site, which was used to initiate styrene to obtain living star-block-linear polystyrene diblock polymers. The living diblock was radially linked by the addition of CDMSS through another convergent process. The resulting polymers were purified by fractionation. The success of the synthesis was demonstrated by the molecular weight progression (gel permeation chromatography with multiangle laser light scattering detection). Glass transition temperature behavior relates to the end-group concentration combined with the effect of the branch points. Dilute solution properties studied by viscometry demonstrate that the polymers have lower intrinsic viscosity values than regular star-shaped polymers.