Cyclins are the activators of cyclin-dependent kinase (CDK) complex, but they also act as docking scaffolds for different short linear motifs (SLiMs) in CDK substrates and inhibitors. According to the unified model of CDK function, the cell cycle is coordinated by CDK both via general CDK activity thresholds and cyclin-specific substrate docking. Recently, it was found that the G1-cyclins of S. cerevisiae have a specific function in promoting polarization and growth of the buds, making the G1 cyclins essential for cell survival. Thus, while a uniform CDK specificity of a single cyclin can be sufficient to drive the cell cycle in some cells, such as in fission yeast, cyclin specificity can be essential in other organisms. However, the known G1-CDK specific LP docking motif, was not responsible for this essential function, indicating that G1-CDKs use yet other unknown docking mechanisms. Here we report a discovery of a G1 cyclin-specific (Cln1,2) lysine-arginine-rich helical docking motif (the K/R motif) in G1-CDK targets involved in the mating pathway (Ste7), transcription (Xbp1), bud morphogenesis (Bud2) and spindle pole body (Spc29, Spc42, Spc110, Sli15) function of S. cerevisiae. We also show that the docking efficiency of K/R motif can be regulated by basophilic kinases such as protein kinase A. Our results further widen the list of cyclin specificity mechanisms and may explain the recently demonstrated unique essential function of G1 cyclins in budding yeast.