The paper is devoted to solutions of a two-person bargaining problem. A solution is a mapping, transforming every convex set \(S\subset R^ 2_+\) into a vector \(s\in S\). We say that the game T is better than the game S for, e.g., player 2, if for every utility level u of player 1 the player 2 can receive at least as much utility in T as in S. The solution is called partially monotonic if for all pairs for which T is better than S for the i-th player this player receives in T the same or more than in S. This request seems quite natural at first sight, but e.g. the Nash solution (uniquely determined by natural symmetry conditions) is not monotonic in this sense; moreover, the only known partially monotonic solution is that of Kalai-Smorodinsky. The author shows that it is really the only continuous partially monotonic solution. In this way a new axiomatization of this solution is obtained, in which, unlike to other known characterizations, the axioms of symmetry and independence of linear transformations are not explicitely assumed.