We define a classical style, one-pass tableau for the full branching-time logic CTL?. This work extends previously defined tableau technique for propositional linear-time temporal logic, PLTL, giving a new decision procedure for CTL?. One of the core features of this method is that unlike any other known deduction for the full branching-time logic, it does not require any additional structures to deal with eventualities. Consequently the presented tableau method opens prospect for defining a dual sequent calculus which is cut-free and, in particular, invariant-free. We also hope that this tableau method could serve as a first-step towards an invariant-free resolution method for CTL*.