The paper estimates the number of states in an unambiguous finite automaton (UFA) that is sufficient and in the worst case necessary to simulate an n-state two-way deterministic finite automaton (2DFA). It is proved that a 2DFA with n states can be transformed to a UFA with fewer than 2ⁿ· n! states. On the other hand, for every n, there is a language recognized by an n-state 2DFA that requires a UFA with at least Ω((42)n·n-1/2) states. The latter result is proved by estimating the rank of a certain matrix.