This paper considers Rubinstein bargaining, with the number of bargainers \(n> 2\). The main result is that if the first player to propose can make either conditional or unconditional offers, then there exists a unique subgame perfect bargaining equilibrium. This result extends Rubinstein's for \(n= 2\) case, as well as \textit{V. Krishna} and \textit{R. Serrano} [Rev. Econ. Stud. 63, 61--80 (1996; Zbl 0844.90122)] in a related \(n\)-player game.