The first theoretical observation of the tricritical point for the rotator-I to rotator-V phase transition of normal alkalies is reported. The influence of pressure on the rotator-II-rotator-I-rotator-V phase sequence in normal alkalies has been studied within the Landau phenomenological theory. Our results show that for a particular value of pressure the first-order rotator-I to rotator-V phase transition becomes second-order at a tricritical point. We outline how the novel phase diagram could be detected experimentally.